InfoVis:Wiki - User contributions [en]

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-17T23:00:45Z

UE-InfoVis1011 0625039: /* Analysis of the tasks */

== Interactive visualization ==

=== Introduction ===
Based on a report [1] of the Unicef, who tries to enable a greater access to drinking-water and sanitation for people all over the world.
A visualization was created that shows the access to these resources in addition to the amount of population.
The situation of the urban population is by far better, in comparison to the rural population.
The main reason behind this are the worse living conditions of the rural population.

884 Million people do not use improved sources of drinking - water.
2.6 Billion people do not use improved sanitation, just 61 percent of human civilization have access to improved sanitation.
With this in mind a visualization was created which enables the viewer an easy way to view and understand the presented data.

The visualization can be found here:
* http://mikazuki.github.com/infovis-ws2010-ex3

=== Analysis of the dataset ===
The dataset[2] is contains datapoints for the years 1990, 1995, 2000, 2005 and 2008.

Some data instances had missing values. Therefore just complete data instances were used.

The main characteristics of the dataset are:
* multivariate
* temporal
* mostly numeric values (except country names)
* hierarchies
** countries are part of continents
** piped and other are part of improved for water
** open defecation, shared and other are part of unimproved

The composition of the data is the following:
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
*** unimproved
** sanitation
*** improved
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== Analysis of the users ===
The main audience for the created visualization are people with interest in global politics. But also viewers with an other background should be able to use the visualization and find the information they need in a fast way.
The visualization mainly focuses on showing the viewer the development of the attributes, so that users are able to investigate how the conditions changed over time.

=== Analysis of the tasks ===

The main intend behind this is to show how the attributes develop over time in the single countries and continents.
A easy away has to be provided, comparing the development of single countries, to find out which countries are in need of humanitary help.

Different questions can be answered by this interactive visualization, e.g.:

* Which continent has more access to important resources?
* How has the growth of access to a resource in a continent improved that the countries on that continent?
* How much did a specific attribute grow in the last few years?

=== Visualization design ===
The Job Voyager[3] visualization was chosen as basis for the created visualization. The main focus is to represent a stacked time series of the data.
The data which should be shown can be filtered by population and its attributes.
The visualization mainly consists of two charts.
The first one shows the attribut development for the continents. The user is able to move the mouse over single continentes to display the name of this continent. It's also possible to select a continent by clicking.
If a continent is selected a second chart compares the development of the countries of this continent.
If the user is moving the mouse over the area of a country, the actual name of the country is shown as label in the left upper corner of the chart.
The values of the different years are shown as additional permanent labels inside the chart.

[[Image:screenshot_job_voyager.png|thumb|300px|left|Figure 1: visualization]]

advantages
* main focus on development over time
* the ability to extend the chart
* main information on one site
* fluent workflow
* dependencies of different variables
* big dataset shown in an easy to understand way

disatvantages
* big differences among attributes are hard to represent
* many countries in one chart are confusing sometimes
* details hard to read
* sometimes difficult to find a specific country

=== Conclusion ===

The chosen visualization focuses on time oriented data. Main focus was to show the development of the specific attributes over time.
Overall the visualization satisfies this purpose in an easy readable way.

=== References ===
:[1] [Unicef, 2010] Unicef. Progress on Sanitation and drinking-water: 2010 Update. ''JMP report - World Health Organization and UNICEF 2010'', 1–55, 2010.http://www.wssinfo.org/fileadmin/user_upload/resources/1278061137-JMP_report_2010_en.pdf.

:[2] [WHO, Unicef, 2003-2010] WHO - UNICEF. Protovis: Joint Monitoring Programme (JMP) for Water Supply and Sanitation. Created at: 1990. Retrieved at: January 15, 2011. http://www.wssinfo.org/data-estimates/table/.

:[3] [Bostock, Heer, 2009] Michael Bostock and Jeffrey Heer. Protovis: A graphical tool for visualization. Created at: March 31, 2009. Retrieved at: January 15, 2011. http://vis.stanford.edu/protovis/ex/jobs.html.

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-17T22:56:21Z

UE-InfoVis1011 0625039: /* Analysis of the users */

== Interactive visualization ==

=== Introduction ===
Based on a report [1] of the Unicef, who tries to enable a greater access to drinking-water and sanitation for people all over the world.
A visualization was created that shows the access to these resources in addition to the amount of population.
The situation of the urban population is by far better, in comparison to the rural population.
The main reason behind this are the worse living conditions of the rural population.

884 Million people do not use improved sources of drinking - water.
2.6 Billion people do not use improved sanitation, just 61 percent of human civilization have access to improved sanitation.
With this in mind a visualization was created which enables the viewer an easy way to view and understand the presented data.

The visualization can be found here:
* http://mikazuki.github.com/infovis-ws2010-ex3

=== Analysis of the dataset ===
The dataset[2] is contains datapoints for the years 1990, 1995, 2000, 2005 and 2008.

Some data instances had missing values. Therefore just complete data instances were used.

The main characteristics of the dataset are:
* multivariate
* temporal
* mostly numeric values (except country names)
* hierarchies
** countries are part of continents
** piped and other are part of improved for water
** open defecation, shared and other are part of unimproved

The composition of the data is the following:
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
*** unimproved
** sanitation
*** improved
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== Analysis of the users ===
The main audience for the created visualization are people with interest in global politics. But also viewers with an other background should be able to use the visualization and find the information they need in a fast way.
The visualization mainly focuses on showing the viewer the development of the attributes, so that users are able to investigate how the conditions changed over time.

=== Analysis of the tasks ===

The main purpose of the used visualization is to show the development over time. The main intend behind this is to show how the attributes develop over time in the single countries and continents.
A easy away has to be provided, comparing the development of single countries, to find out which countries are in need of humanitary help.

Different questions can be answered by this interactive visualization, e.g.:
Are there any dependencies of attributes, which affect different countries?
Which continent has more access to important resources?
How much did a specific attribute grow in the last few years?

=== Visualization design ===
The Job Voyager[3] visualization was chosen as basis for the created visualization. The main focus is to represent a stacked time series of the data.
The data which should be shown can be filtered by population and its attributes.
The visualization mainly consists of two charts.
The first one shows the attribut development for the continents. The user is able to move the mouse over single continentes to display the name of this continent. It's also possible to select a continent by clicking.
If a continent is selected a second chart compares the development of the countries of this continent.
If the user is moving the mouse over the area of a country, the actual name of the country is shown as label in the left upper corner of the chart.
The values of the different years are shown as additional permanent labels inside the chart.

[[Image:screenshot_job_voyager.png|thumb|300px|left|Figure 1: visualization]]

advantages
* main focus on development over time
* the ability to extend the chart
* main information on one site
* fluent workflow
* dependencies of different variables
* big dataset shown in an easy to understand way

disatvantages
* big differences among attributes are hard to represent
* many countries in one chart are confusing sometimes
* details hard to read
* sometimes difficult to find a specific country

=== Conclusion ===

The chosen visualization focuses on time oriented data. Main focus was to show the development of the specific attributes over time.
Overall the visualization satisfies this purpose in an easy readable way.

=== References ===
:[1] [Unicef, 2010] Unicef. Progress on Sanitation and drinking-water: 2010 Update. ''JMP report - World Health Organization and UNICEF 2010'', 1–55, 2010.http://www.wssinfo.org/fileadmin/user_upload/resources/1278061137-JMP_report_2010_en.pdf.

:[2] [WHO, Unicef, 2003-2010] WHO - UNICEF. Protovis: Joint Monitoring Programme (JMP) for Water Supply and Sanitation. Created at: 1990. Retrieved at: January 15, 2011. http://www.wssinfo.org/data-estimates/table/.

:[3] [Bostock, Heer, 2009] Michael Bostock and Jeffrey Heer. Protovis: A graphical tool for visualization. Created at: March 31, 2009. Retrieved at: January 15, 2011. http://vis.stanford.edu/protovis/ex/jobs.html.

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-17T22:46:08Z

UE-InfoVis1011 0625039: /* Analysis of the dataset */

== Interactive visualization ==

=== Introduction ===
Based on a report [1] of the Unicef, who tries to enable a greater access to drinking-water and sanitation for people all over the world.
A visualization was created that shows the access to these resources in addition to the amount of population.
The situation of the urban population is by far better, in comparison to the rural population.
The main reason behind this are the worse living conditions of the rural population.

884 Million people do not use improved sources of drinking - water.
2.6 Billion people do not use improved sanitation, just 61 percent of human civilization have access to improved sanitation.
With this in mind a visualization was created which enables the viewer an easy way to view and understand the presented data.

The visualization can be found here:
* http://mikazuki.github.com/infovis-ws2010-ex3

=== Analysis of the dataset ===
The dataset[2] is contains datapoints for the years 1990, 1995, 2000, 2005 and 2008.

Some data instances had missing values. Therefore just complete data instances were used.

The main characteristics of the dataset are:
* multivariate
* temporal
* mostly numeric values (except country names)
* hierarchies
** countries are part of continents
** piped and other are part of improved for water
** open defecation, shared and other are part of unimproved

The composition of the data is the following:
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
*** unimproved
** sanitation
*** improved
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== Analysis of the users ===
The main audience for the created visualization are people with interest in global politics. But also viewers with a lower background should be able to use the visualization and find the information they need in a fast way.
The visualization mainly focuses on showing the viewer the development of the attributes, so that users are able to investigate how the conditions changed over time.

=== Analysis of the tasks ===

The main purpose of the used visualization is to show the development over time. The main intend behind this is to show how the attributes develop over time in the single countries and continents.
A easy away has to be provided, comparing the development of single countries, to find out which countries are in need of humanitary help.

Different questions can be answered by this interactive visualization, e.g.:
Are there any dependencies of attributes, which affect different countries?
Which continent has more access to important resources?
How much did a specific attribute grow in the last few years?

=== Visualization design ===
The Job Voyager[3] visualization was chosen as basis for the created visualization. The main focus is to represent a stacked time series of the data.
The data which should be shown can be filtered by population and its attributes.
The visualization mainly consists of two charts.
The first one shows the attribut development for the continents. The user is able to move the mouse over single continentes to display the name of this continent. It's also possible to select a continent by clicking.
If a continent is selected a second chart compares the development of the countries of this continent.
If the user is moving the mouse over the area of a country, the actual name of the country is shown as label in the left upper corner of the chart.
The values of the different years are shown as additional permanent labels inside the chart.

[[Image:screenshot_job_voyager.png|thumb|300px|left|Figure 1: visualization]]

advantages
* main focus on development over time
* the ability to extend the chart
* main information on one site
* fluent workflow
* dependencies of different variables
* big dataset shown in an easy to understand way

disatvantages
* big differences among attributes are hard to represent
* many countries in one chart are confusing sometimes
* details hard to read
* sometimes difficult to find a specific country

=== Conclusion ===

The chosen visualization focuses on time oriented data. Main focus was to show the development of the specific attributes over time.
Overall the visualization satisfies this purpose in an easy readable way.

=== References ===
:[1] [Unicef, 2010] Unicef. Progress on Sanitation and drinking-water: 2010 Update. ''JMP report - World Health Organization and UNICEF 2010'', 1–55, 2010.http://www.wssinfo.org/fileadmin/user_upload/resources/1278061137-JMP_report_2010_en.pdf.

:[2] [WHO, Unicef, 2003-2010] WHO - UNICEF. Protovis: Joint Monitoring Programme (JMP) for Water Supply and Sanitation. Created at: 1990. Retrieved at: January 15, 2011. http://www.wssinfo.org/data-estimates/table/.

:[3] [Bostock, Heer, 2009] Michael Bostock and Jeffrey Heer. Protovis: A graphical tool for visualization. Created at: March 31, 2009. Retrieved at: January 15, 2011. http://vis.stanford.edu/protovis/ex/jobs.html.

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-17T22:43:51Z

UE-InfoVis1011 0625039: /* Introduction */

== Interactive visualization ==

=== Introduction ===
Based on a report [1] of the Unicef, who tries to enable a greater access to drinking-water and sanitation for people all over the world.
A visualization was created that shows the access to these resources in addition to the amount of population.
The situation of the urban population is by far better, in comparison to the rural population.
The main reason behind this are the worse living conditions of the rural population.

884 Million people do not use improved sources of drinking - water.
2.6 Billion people do not use improved sanitation, just 61 percent of human civilization have access to improved sanitation.
With this in mind a visualization was created which enables the viewer an easy way to view and understand the presented data.

The visualization can be found here:
* http://mikazuki.github.com/infovis-ws2010-ex3

=== Analysis of the dataset ===
The dataset[2] is contains datapoints for the years 1990, 1995, 2000, 2005 and 2008.

Some data instances had missing values. Therefore just complete data instances were used.

The main characteristics of the dataset are:
* multivariate
* temporal
* numeric
* hierarchies
* countries < continents

The composition of the data is the following:
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
** sanitation
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== Analysis of the users ===
The main audience for the created visualization are people with interest in global politics. But also viewers with a lower background should be able to use the visualization and find the information they need in a fast way.
The visualization mainly focuses on showing the viewer the development of the attributes, so that users are able to investigate how the conditions changed over time.

=== Analysis of the tasks ===

The main purpose of the used visualization is to show the development over time. The main intend behind this is to show how the attributes develop over time in the single countries and continents.
A easy away has to be provided, comparing the development of single countries, to find out which countries are in need of humanitary help.

Different questions can be answered by this interactive visualization, e.g.:
Are there any dependencies of attributes, which affect different countries?
Which continent has more access to important resources?
How much did a specific attribute grow in the last few years?

=== Visualization design ===
The Job Voyager[3] visualization was chosen as basis for the created visualization. The main focus is to represent a stacked time series of the data.
The data which should be shown can be filtered by population and its attributes.
The visualization mainly consists of two charts.
The first one shows the attribut development for the continents. The user is able to move the mouse over single continentes to display the name of this continent. It's also possible to select a continent by clicking.
If a continent is selected a second chart compares the development of the countries of this continent.
If the user is moving the mouse over the area of a country, the actual name of the country is shown as label in the left upper corner of the chart.
The values of the different years are shown as additional permanent labels inside the chart.

[[Image:screenshot_job_voyager.png|thumb|300px|left|Figure 1: visualization]]

advantages
* main focus on development over time
* the ability to extend the chart
* main information on one site
* fluent workflow
* dependencies of different variables
* big dataset shown in an easy to understand way

disatvantages
* big differences among attributes are hard to represent
* many countries in one chart are confusing sometimes
* details hard to read
* sometimes difficult to find a specific country

=== Conclusion ===

The chosen visualization focuses on time oriented data. Main focus was to show the development of the specific attributes over time.
Overall the visualization satisfies this purpose in an easy readable way.

=== References ===
:[1] [Unicef, 2010] Unicef. Progress on Sanitation and drinking-water: 2010 Update. ''JMP report - World Health Organization and UNICEF 2010'', 1–55, 2010.http://www.wssinfo.org/fileadmin/user_upload/resources/1278061137-JMP_report_2010_en.pdf.

:[2] [WHO, Unicef, 2003-2010] WHO - UNICEF. Protovis: Joint Monitoring Programme (JMP) for Water Supply and Sanitation. Created at: 1990. Retrieved at: January 15, 2011. http://www.wssinfo.org/data-estimates/table/.

:[3] [Bostock, Heer, 2009] Michael Bostock and Jeffrey Heer. Protovis: A graphical tool for visualization. Created at: March 31, 2009. Retrieved at: January 15, 2011. http://vis.stanford.edu/protovis/ex/jobs.html.

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-17T22:42:06Z

UE-InfoVis1011 0625039: /* Analysis of the dataset */ updated year description

== Interactive visualization ==

=== Introduction ===
Based on a report [1] of the Unicef, who tries to enable a greater access to drinking-water and sanitation for people all over the world, a visualization was created, which shows the access to these resources in addition to the amount of population. The situation of the urban population is by far better, in comparison to the rural population. The main reason behind this are the worse living conditions of the rural population.

884 Million people do not use improved sources of drinking - water.
2.6 Billion people do not use improved sanitation, just 61 percent of human civilization have access to improved sanitation.
With this in mind a visualization was created which enables the viewer an easy way to view and understand the presented data.

The visualization can be found here:
* http://mikazuki.github.com/infovis-ws2010-ex3

=== Analysis of the dataset ===
The dataset[2] is contains datapoints for the years 1990, 1995, 2000, 2005 and 2008.

Some data instances had missing values. Therefore just complete data instances were used.

The main characteristics of the dataset are:
* multivariate
* temporal
* numeric
* hierarchies
* countries < continents

The composition of the data is the following:
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
** sanitation
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== Analysis of the users ===
The main audience for the created visualization are people with interest in global politics. But also viewers with a lower background should be able to use the visualization and find the information they need in a fast way.
The visualization mainly focuses on showing the viewer the development of the attributes, so that users are able to investigate how the conditions changed over time.

=== Analysis of the tasks ===

The main purpose of the used visualization is to show the development over time. The main intend behind this is to show how the attributes develop over time in the single countries and continents.
A easy away has to be provided, comparing the development of single countries, to find out which countries are in need of humanitary help.

Different questions can be answered by this interactive visualization, e.g.:
Are there any dependencies of attributes, which affect different countries?
Which continent has more access to important resources?
How much did a specific attribute grow in the last few years?

=== Visualization design ===
The Job Voyager[3] visualization was chosen as basis for the created visualization. The main focus is to represent a stacked time series of the data.
The data which should be shown can be filtered by population and its attributes.
The visualization mainly consists of two charts.
The first one shows the attribut development for the continents. The user is able to move the mouse over single continentes to display the name of this continent. It's also possible to select a continent by clicking.
If a continent is selected a second chart compares the development of the countries of this continent.
If the user is moving the mouse over the area of a country, the actual name of the country is shown as label in the left upper corner of the chart.
The values of the different years are shown as additional permanent labels inside the chart.

[[Image:screenshot_job_voyager.png|thumb|300px|left|Figure 1: visualization]]

advantages
* main focus on development over time
* the ability to extend the chart
* main information on one site
* fluent workflow
* dependencies of different variables
* big dataset shown in an easy to understand way

disatvantages
* big differences among attributes are hard to represent
* many countries in one chart are confusing sometimes
* details hard to read
* sometimes difficult to find a specific country

=== Conclusion ===

The chosen visualization focuses on time oriented data. Main focus was to show the development of the specific attributes over time.
Overall the visualization satisfies this purpose in an easy readable way.

=== References ===
:[1] [Unicef, 2010] Unicef. Progress on Sanitation and drinking-water: 2010 Update. ''JMP report - World Health Organization and UNICEF 2010'', 1–55, 2010.http://www.wssinfo.org/fileadmin/user_upload/resources/1278061137-JMP_report_2010_en.pdf.

:[2] [WHO, Unicef, 2003-2010] WHO - UNICEF. Protovis: Joint Monitoring Programme (JMP) for Water Supply and Sanitation. Created at: 1990. Retrieved at: January 15, 2011. http://www.wssinfo.org/data-estimates/table/.

:[3] [Bostock, Heer, 2009] Michael Bostock and Jeffrey Heer. Protovis: A graphical tool for visualization. Created at: March 31, 2009. Retrieved at: January 15, 2011. http://vis.stanford.edu/protovis/ex/jobs.html.

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-14T20:16:30Z

UE-InfoVis1011 0625039: /* data */

== interactive visualization ==

... whatever ...

=== Introduction ===

...

=== data ===
progress on sanitation and drinking water

* multivariate
* temporal
* numeric
* hierarchies
* countries < continents
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
** sanitation
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== users ===
...

=== tasks ===
...

=== visualization design ===
...

=== Conclusion ===
...

=== References ===
...

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-14T20:06:08Z

UE-InfoVis1011 0625039: /* data */

== interactive visualization ==

... whatever ...

=== Introduction ===

...

=== data ===
progress on sanitation and drinking water

* multivariate
* temporal
* numeric
* hierarchies
* all data (totals)
** urban
** rural
** water
*** improved (totals)
**** piped
**** other improved
** sanitation
*** unimproved (totals)
**** open defecation
**** shared
**** other

=== users ===
...

=== tasks ===
...

=== visualization design ===
...

=== Conclusion ===
...

=== References ===
...

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3

2011-01-14T19:56:24Z

UE-InfoVis1011 0625039: data description draft

== interactive visualization ==

... whatever ...

=== Introduction ===

...

=== data ===
progress on sanitation and drinking water

* multivariate
* temporal
* numeric
* hierarchies
** water
*** improved
**** piped
**** other improved
** sanitation
*** unimproved
**** open defecation
**** shared
**** other

=== users ===
...

=== tasks ===
...

=== visualization design ===
...

=== Conclusion ===
...

=== References ===
...

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T22:42:44Z

UE-InfoVis1011 0625039: /* Conclusion */ typos

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] page 1018.]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works very well for categorical axes and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the parallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order to compare the metric with different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value. See the right histograms in figure 2. [[Image:Dasgupta+Kosara_Distance+angle-histograms.png|thumb|300px|Figure 2: "Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data." See [Dasgupta and Kosara, 2010] page 1021.]]

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.
:Narrowly distributed histograms have high parallelism. See the left histograms figure 2. Between horsepower and weight there is high parallelism. Between the other axes not.

;Mutual Information
:Mutual Information measures the statistical dependence of the drawn data. Pargnostics treats the data dimensions as random variables and uses the two-dimensional axis histogram to denote the joint probability of random variables. This metric's value should be maximized.

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left axis.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:This metric shows the degree of randomness in any segment of a visualization. A high pixel-based entropy normally leads to busy but very readable displays of data. [Dasgupta and Kosara, 2010]

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates, which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix, which is constructed at the beginning of the algorithm, they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are an important step towards better visualiztions.
These metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T22:32:24Z

UE-InfoVis1011 0625039: /* Metrics */

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] page 1018.]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works very well for categorical axes and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the parallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order to compare the metric with different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value. See the right histograms in figure 2. [[Image:Dasgupta+Kosara_Distance+angle-histograms.png|thumb|300px|Figure 2: "Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data." See [Dasgupta and Kosara, 2010] page 1021.]]

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.
:Narrowly distributed histograms have high parallelism. See the left histograms figure 2. Between horsepower and weight there is high parallelism. Between the other axes not.

;Mutual Information
:Mutual Information measures the statistical dependence of the drawn data. Pargnostics treats the data dimensions as random variables and uses the two-dimensional axis histogram to denote the joint probability of random variables. This metric's value should be maximized.

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:This metric shows the degree of randomness in any segment of a visualization. A high pixel-based entropy based entropy normally leads to busy but very readable displays of data. [Dasgupta and Kosara, 2010]

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates, which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix, which is constructed at the beginning of the algorithm, they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are an important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T22:23:58Z

UE-InfoVis1011 0625039: /* Metrics */ rephrase mutal information

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] page 1018.]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works very well for categorical axes and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the parallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order to compare the metric with different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value. See the right histograms in figure 2. [[Image:Dasgupta+Kosara_Distance+angle-histograms.png|thumb|300px|Figure 2: "Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data." See [Dasgupta and Kosara, 2010] page 1021.]]

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.
:Narrowly distributed histograms have high parallelism. See the left histograms figure 2. Between horsepower and weight there is high parallelism. Between the other axes not.

;Mutual Information
:Mutual Information measures the statistical dependence of the drawn data. Pargnostics treats the data dimensions as random variables and uses the two-dimensional axis histogram to denote the joint probability of random variables. This metric's value should be maximized.

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:This metric shows the degree of randomness in any segment of a visualization.

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates, which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix, which is constructed at the beginning of the algorithm, they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are an important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:57:12Z

UE-InfoVis1011 0625039: /* Metrics */ Added image for angles & parallelism

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] page 1018.]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works very well for categorical axes and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the parallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order to compare the metric with different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value. See the right histograms in figure 2. [[Image:Dasgupta+Kosara_Distance+angle-histograms.png|thumb|300px|Figure 2: "Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data." See [Dasgupta and Kosara, 2010] page 1021.]]

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.
:Narrowly distributed histograms have high parallelism. See the left histograms figure 2. Between horsepower and weight there is high parallelism. Between the other axes not.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix which is constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are an important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

File:Dasgupta+Kosara Distance+angle-histograms.png

2010-11-17T21:50:07Z

UE-InfoVis1011 0625039: quotation marks

== Summary ==
"Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data." See [Dasgupta and Kosara, 2010] page 1021.
== Copyright status ==
Aritra Dasgupta and Robert Kosara 2010
== Source ==
[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics, 16(6):1017-1026, November/December 2010

File:Dasgupta+Kosara Distance+angle-histograms.png

2010-11-17T21:49:43Z

UE-InfoVis1011 0625039: Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data. See [Dasgupta and Kosara, 2010] page 1021.

== Summary ==
Distance histograms (left half of each cell below the parallel coordinates) and angles of crossings (right half) histograms for different dimensions of the cars data. See [Dasgupta and Kosara, 2010] page 1021.
== Copyright status ==
Aritra Dasgupta and Robert Kosara 2010
== Source ==
[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics, 16(6):1017-1026, November/December 2010

File:Dasgupta+Kosara Pixel-Space Histograms.png

2010-11-17T21:49:35Z

UE-InfoVis1011 0625039: summary updated

== Summary ==
"Illustrating binning with equal width histograms: On the left is the binned space of the parallel coordinates and on the right is the degree of each bin in the 2D histogram." See [Dasgupta and Kosara, 2010] page 1018.
== Copyright status ==
Aritra Dasgupta and Robert Kosara 2010
== Source ==
[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics, 16(6):1017-1026, November/December 2010

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:42:44Z

UE-InfoVis1011 0625039: /* Conclusion */ typos

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works for categorical axes very well and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix which is constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are an important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:41:40Z

UE-InfoVis1011 0625039: /* Branch-and-Bound Optimization */ typos

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' states that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works for categorical axes very well and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The branch-and-bound algorithm uses a priority queue and best-first search.
For that kind of implementations it's very important to make precise estimates which subtrees can be culled and which can't.
Since these estimates are based on the full cost matrix which is constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:39:32Z

UE-InfoVis1011 0625039: /* Axis Inversions */ Typos/formulation

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works for categorical axes very well and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taken into account.
The state - inverted or not inverted - with the lower cost is used in the matrix and the algorithm keeps track which one it was.
This happens locally so inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:36:45Z

UE-InfoVis1011 0625039: /* Pargnostics: Screen-Space Metrics for Parallel Coordinates */ moved axis inversion & branchbound opt one heading level deeper

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
First ''pixel-space histograms'' are calculated to optimize the calculation of these metrics.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

One of the most useful optimization is the line crossing and the parallelism metrics. Angels of crossing helps out, where line crossing gets difficult to read.
The convergence-divergence metric works for categorical axes very well and the pixel based entropy optimizes the alpha value, which is useful on larger datasets.

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

==== Axis Inversions ====

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

==== Branch-and-Bound Optimization ====

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:33:01Z

UE-InfoVis1011 0625039: /* Dimension Order Optimization */ Typos fixed

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this visual structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visualizations have to show the relevant information at the first glance and therefore show the information in a clear structure.
Until now not a lot of attention is paid to the way a visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For optimize calculation of these metrics, first ''pixel-space histograms'' are calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
This is an NP-complete problem, but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions [Dasgupta and Kosara, 2010].
Using a branch-and-bound algorithm also can reduce the time necessary.

The purpose of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:26:16Z

UE-InfoVis1011 0625039: /* Introduction */ fixed typos and added reference

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete pixels.
The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided.
But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good visuals have to show the relevant information at the first glance and therefore they have to show the information in a clear structure.
Until now not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts. [Dasgupta and Kosara, 2010]

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For optimize calculation of these metrics, first ''pixel-space histograms'' are calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized to increase the quality of the visualization.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:17:42Z

UE-InfoVis1011 0625039: /* Metrics */ removed unnecessary introductory sentences

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For optimize calculation of these metrics, first ''pixel-space histograms'' are calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:This metric intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations. [Dasgupta and Kosara, 2010]

;Angles of Crossing
:Lines crossing at flat angles tend to create clutter [Dasgupta and Kosara, 2010]. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:14:33Z

UE-InfoVis1011 0625039: /* Metrics */ Over-plotting

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For optimize calculation of these metrics, first ''pixel-space histograms'' are calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:The first metric proposed by Dasgupta and Kosara [2010] is number of line crossings. This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

;Angles of Crossing
:Angles of crossing is a metric equally important to the number of line crossings [Dasgupta and Kosara, 2010]. Lines crossing at flat angles tend to create clutter. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:Over-plotting measures how many lines are aggregated on a single pixel when the parallel coordinates are drawn. This metric is directly dependent on the number of bins (pixels) used for an axis [Dasgupta and Kosara, 2010]. The value obtained by this metric should be minimized.

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:06:55Z

UE-InfoVis1011 0625039: /* Metrics */ references

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:The first metric proposed by Dasgupta and Kosara [2010] is number of line crossings. This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

;Angles of Crossing
:Angles of crossing is a metric equally important to the number of line crossings [Dasgupta and Kosara, 2010]. Lines crossing at flat angles tend to create clutter. To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter [Dasgupta and Kosara, 2010]. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:TBD
:TBD

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T21:02:42Z

UE-InfoVis1011 0625039: /* Metrics */ convergence/divergence draft

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:The first metric proposed by Dasgupta and Kosara [2010] is number of line crossings. This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

;Angles of Crossing
:Angles of crossing is a metric equally important to the number of line crossings. Lines crossing at flat angles tend to create clutter.To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism can for example show clusters within a subset of the data. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:Lines from the left axis joining in single points on the right axis are converging. Divergence is the inverse of this - i.e. lines from the right joining on the left.

;Over-plotting
:TBD
:TBD

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T20:55:16Z

UE-InfoVis1011 0625039: /* Metrics */ reformulated angle crossing & parallelism

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:The first metric proposed by Dasgupta and Kosara [2010] is number of line crossings. This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

;Angles of Crossing
:Angles of crossing is a metric equally important to the number of line crossings. Lines crossing at flat angles tend to create clutter.To calculate this metric, first the crossing angles between every pair of lines which are crossing get calculated. From the results of these calculations the median crossing angle is obtained to be used as the resulting metric value.

;Parallelism
:A pair of lines which is not crossing is parallel to each other. Parallelism can for example show clusters within a subset of the data. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter. Parallelism is calculated by taking the inverse of the absolute interquartile range of line distances.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:

;Over-plotting
:TBD
:TBD

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T20:42:27Z

UE-InfoVis1011 0625039: /* Metrics */ changed formatting for metrics to list

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

;Number of Line Crossings
:The first metric proposed by Dasgupta and Kosara [2010] is number of line crossings. This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates. The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''. This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

;Angles of Crossing
:The number of line crossings is one one of the most important metrics. But according to Dasgupta and Kosara [2010] the angles of the line crossings are an equally important metric. Lines crossing at flat angles tend to create clutter. But how does this metric gets calculated? First the crossing angles between every pair of lines which are crossing get calculated. Afterwards the median crossing angle gets calculated. This median can be used for optimizations.

;Parallelism
:Another metric is Parallelism. A pair of lines which is not crossing is parallel to each other. Parallelism can for example show clusters within a subset of the data. Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter.

;Mutual Information
:TBD
:TBD

;Convergence, Divergence
:TBD
:TBD

;Over-plotting
:TBD
:TBD

;Pixel-based Entropy
:TBD
:TBD

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really important step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T20:37:36Z

UE-InfoVis1011 0625039: /* Conclusion */

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

==== Number of Line Crossings ====

The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

==== Angles of Crossing ====

The number of line crossings is one one of the most important metrics.
But according to Dasgupta and Kosara [2010] the angles of the line crossings are an equally important metric.
Lines crossing at flat angles tend to create clutter.
But how does this metric gets calculated?
First the crossing angles between every pair of lines which are crossing get calculated.
Afterwards the median crossing angle gets calculated. This median can be used for optimizations.

==== Parallelism ====

Another metric is Parallelism. A pair of lines which is not crossing is parallel to each other.
Parallelism can for example show clusters within a subset of the data.
Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter.

==== Mutual Information ====

==== Convergence, Divergence ====

==== Over-plotting ====

==== Pixel-based Entropy ====

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|In this sense, Pargnostics fills a gap in the existing literature on parallel coordinates. Being able to analyze what ends up on the screen makes it possible to provide better visualization setups that take the specific properties of the visualization technique into account.|Dasgupta and Kosara, 2010}}

The metrics and the optimization explained above are a really importan step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T20:36:32Z

UE-InfoVis1011 0625039: /* Conclusion */ formatting of quotation

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

==== Number of Line Crossings ====

The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

==== Angles of Crossing ====

The number of line crossings is one one of the most important metrics.
But according to Dasgupta and Kosara [2010] the angles of the line crossings are an equally important metric.
Lines crossing at flat angles tend to create clutter.
But how does this metric gets calculated?
First the crossing angles between every pair of lines which are crossing get calculated.
Afterwards the median crossing angle gets calculated. This median can be used for optimizations.

==== Parallelism ====

Another metric is Parallelism. A pair of lines which is not crossing is parallel to each other.
Parallelism can for example show clusters within a subset of the data.
Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter.

==== Mutual Information ====

==== Convergence, Divergence ====

==== Over-plotting ====

==== Pixel-based Entropy ====

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

{{Quotation|"In this sense, Pargnostics fills a gap in the existing literature
on parallel coordinates. Being able to analyze what ends up on
the screen makes it possible to provide better visualization setups that
take the specific properties of the visualization technique into account."
|[Dasgupta and Kosara, 2010]}}

The metrics and the optimization explained above are a really importan step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-17T20:35:26Z

UE-InfoVis1011 0625039: /* References */ fixed typo

== Pargnostics: Screen-Space Metrics for Parallel Coordinates ==

=== Introduction ===

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Good Visuals have to show the relevant information at the first glance and therefor they have to show the information in a clear structure.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

=== Metrics ===

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

==== Number of Line Crossings ====

The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

==== Angles of Crossing ====

The number of line crossings is one one of the most important metrics.
But according to Dasgupta and Kosara [2010] the angles of the line crossings are an equally important metric.
Lines crossing at flat angles tend to create clutter.
But how does this metric gets calculated?
First the crossing angles between every pair of lines which are crossing get calculated.
Afterwards the median crossing angle gets calculated. This median can be used for optimizations.

==== Parallelism ====

Another metric is Parallelism. A pair of lines which is not crossing is parallel to each other.
Parallelism can for example show clusters within a subset of the data.
Parallelism is often prefered as a metric compared to the number of crossings because it tends to produce less clutter.

==== Mutual Information ====

==== Convergence, Divergence ====

==== Over-plotting ====

==== Pixel-based Entropy ====

=== Dimension Order Optimization ===

Using the metrics from above helps to find an optimization of the visualization display.
Normally this would be a NP-complete problem but by using a binned data model and by considering the special properties of parallel coordinates it's possible to reduce the amount of time which is needed to find optimal solutions. Using a branch-and-bound algorithm also can reduce the necessary time.

The porpuse of the branch-and-bound algorithm is to find the optimal order of axes.
To do that a matrix of all axis pairs and their associated costs gets constructed.
The costs are a combination of several metrics.

The construction of the matrix has to be done only once at the beginning of the algorithm.

=== Axis Inversions ===

While constructing the matrix of axis pairs both the inverted and noninverted situation for every axis pair is taking into account.
The situation(inverted or noninverted) with the lower costs gets used in the matrix and the algorithm keeps track which one that was.
This happens locally. So inverting one axis pair doesn't have an immediate effect on other axis pairs.

=== Branch-and-Bound Optimization ===

The Branch-and-Bound algorithm uses a priority queue and best-first search. For that kind of implemantions it's very important to make precise estimates which subtrees can be culled and which can't. Since these estimates are based on the full cost matrix constructed at the beginning of the algorithm they are indeed very precise.

Based on case studies by Dasgupta and Kosara [2010] the branch-and-bound algorithm finds the optimal solution really quick.
The main reason for this is that the metrics are constructed for every axis pair on their own and not for every possible combination of the axis pairs in the entire visualization.

=== Conclusion ===

<blockquote>"In this sense, Pargnostics fills a gap in the existing literature
on parallel coordinates. Being able to analyze what ends up on
the screen makes it possible to provide better visualization setups that
take the specific properties of the visualization technique into account."</blockquote>
<center>[Dasgupta and Kosara, 2010]</center>

The metrics and the optimization explained above are a really importan step towards better visualiztions.
This metrics not only describe the image which is rendered to screen, but also the different visual structures which can be seen in this image.

=== References ===

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National Conference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T22:27:19Z

UE-InfoVis1011 0625039: /* Over-plotting */

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T22:11:58Z

UE-InfoVis1011 0625039: make all headings one level lower

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:56:20Z

UE-InfoVis1011 0625039: /* References */

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

== Metrics ==

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

=== Number of Line Crossings ===
The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

=== Angles of Crossing ===

=== Parallelism ===

=== Mutual Information ===

=== Convergence, Divergence ===

=== Over-plotting ===

=== Pixel-based Entropy ===

== Dimension Order Optimization ==

== Conclusion ==

== References ==

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and [[Kosara, Robert|Kosara]], 2010] Aritra Dasgupta and [[Kosara, Robert|Robert Kosara]]. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National COnference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:49:57Z

UE-InfoVis1011 0625039: /* Metrics */

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

== Metrics ==

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

=== Number of Line Crossings ===
The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

=== Angles of Crossing ===

=== Parallelism ===

=== Mutual Information ===

=== Convergence, Divergence ===

=== Over-plotting ===

=== Pixel-based Entropy ===

== Dimension Order Optimization ==

== Conclusion ==

== References ==

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National COnference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:47:54Z

UE-InfoVis1011 0625039: /* References */ Add references for measurements part

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

== Metrics ==

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

=== Number of Line Crossings ===
The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

=== Metrics ... ===

* Number of Line Crossings
* Angles of Crossing
* Parallelism
* Mutual Information
* Convergence, Divergence
* Over-plotting
* Pixel-based Entropy

== Dimension Order Optimization ==

== Conclusion ==

== References ==

*[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
*[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010.
*[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National COnference on Artificial Intelligence'', pages 383-388, 1986

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:44:18Z

UE-InfoVis1011 0625039: /* Metrics */ number of line crossings

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

Visualization still takes place in a space with a limited number of discrete
pixels. The result of this often is over-plotting, clutter or other things.
Most of the time this structures are avoided. But sometimes this artifacts can be useful, because they might point out interesting structures in the data.
Until know not a lot of attention is paid to the way visualzation is presented on the screen.
For the case of parallel coordinates so called Pargnostics (Parallel coordinates diagnostics) should act as a bridge between the created visualization and the perceptual system of the user.
Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.

== Metrics ==

[[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
The metrics are used to measure the properties of parallel coordinates.
For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
Pixel-space histograms discretize the lines drawn in parallel coordinates into bins - each bin being one pixel (for a total of ''h'' pixels in an axis):
* ''One-Dimensional Axis Histogram'': A vector ''b'' containing the number of lines that start or end at this pixel - see columns A and B in figure 1.
* ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
* ''Two-Dimensional Axis Pair Histogram'': A matrix where each cell ''xi,j'' means that ''n'' lines are going from pixel ''i'' to pixel ''j'' - see matrix in figure 1.

The metrics proposed can be used for measuring different data properties: ''correlation'' (number of line crossings, angles of crossing), ''aggregation'' (parallelism), ''many-to-one/one-to-many relationships'' (convergence, divergence), ''quality'' (over-plotting), ''information density'' (pixel-based entropy).

=== Number of Line Crossings ===
The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h4)''.
This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.

=== Metrics ... ===

* Number of Line Crossings
* Angles of Crossing
* Parallelism
* Mutual Information
* Convergence, Divergence
* Over-plotting
* Pixel-based Entropy

== Dimension Order Optimization ==

== Conclusion ==

== References ==

[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:33:17Z

UE-InfoVis1011 0625039: /* Metrics */ Optimize space usage

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:32:11Z

UE-InfoVis1011 0625039: /* Metrics */ Added image

File:Dasgupta+Kosara Pixel-Space Histograms.png

2010-11-16T21:23:29Z

UE-InfoVis1011 0625039: Pixel-space histograms

== Summary ==
Pixel-space histograms
== Copyright status ==
Aritra Dasgupta and Robert Kosara 2010
== Source ==
[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics, 16(6):1017-1026, November/December 2010

File:GasguPixel-Space Histograms.png

2010-11-16T21:22:45Z

UE-InfoVis1011 0625039: New page: == Summary == == Copyright status == == Source ==

== Summary ==

== Copyright status ==

== Source ==

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T21:19:41Z

UE-InfoVis1011 0625039: /* Metrics */ draft for metrics/pixelspace histograms

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T20:49:16Z

UE-InfoVis1011 0625039: /* References */ should read bib formatting guide before writing the bib ...

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

== Metrics ==

=== Pixel-Space Histograms ===

* One-Dimensional Axis Histogram
* One-Dimensional Distance Histogram
* Two-Dimensional Axis Pair Histogram

=== Metrics ... ===

* Number of Line Crossings
* Angles of Crossing
* Parallelism
* Mutual Information
* Convergence, Divergence
* Over-plotting
* Pixel-based Entropy

== Dimension Order Optimization ==

== Conclusion ==

== References ==

[Dasgupta and Kosara, 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T20:41:47Z

UE-InfoVis1011 0625039: /* Metrics */ Layout/Excerpt of important points

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

== Metrics ==

=== Pixel-Space Histograms ===

* One-Dimensional Axis Histogram
* One-Dimensional Distance Histogram
* Two-Dimensional Axis Pair Histogram

=== Metrics ... ===

* Number of Line Crossings
* Angles of Crossing
* Parallelism
* Mutual Information
* Convergence, Divergence
* Over-plotting
* Pixel-based Entropy

== Dimension Order Optimization ==

== Conclusion ==

== References ==

[Dasgupta et al., 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T20:36:37Z

UE-InfoVis1011 0625039: /* References */

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

== Metrics ==

== Dimension Order Optimization ==

== Conclusion ==

== References ==

[Dasgupta et al., 2010] Aritra Dasgupta and Robert Kosara. Pargnostics: Screen-Space Metrics for Parallel Coordinates. ''IEEE Transactions on Visualization and Computer Graphics'', 16(6):1017-1026, November/December 2010

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T20:35:52Z

UE-InfoVis1011 0625039:

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2

2010-11-16T20:30:36Z

UE-InfoVis1011 0625039:

= Pargnostics: Screen-Space Metrics for Parallel Coordinates =

== Introduction ==

== Metrics ==

== Dimension Order Optimization ==

== Conclusion ==

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05

2010-10-18T17:00:09Z

UE-InfoVis1011 0625039: Added link to infovis ue homepage

Gruppe 05 für die [[Teaching:TUW_-_UE_InfoVis_WS_2010/11|UE InfoVis WS 2010/11]]

=Gruppenmitglieder=
* [[User:UE-InfoVis1011_0625039|Marschik, Patrick]]
* Alili, Jasin
* Bachhuber, Ben

=Aufgabe=
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 1|Aufgabe 1]] (siehe [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws10/infovis_ue_aufgabe1.html])
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2|Aufgabe 2]] (siehe [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws10/infovis_ue_aufgabe2.html])
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3|Aufgabe 3]] (siehe [http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws10/infovis_ue_aufgabe3.html])

Teaching:TUW - UE InfoVis WS 2010/11

2010-10-18T16:50:14Z

UE-InfoVis1011 0625039: Added link for group 05

[[Image:Aigner03infovis ue.gif]] <big>WS 2010/11</big>

'''LVA Nr:''' 188.308 ([https://tiss.tuwien.ac.at/course/courseDetails.xhtml?courseNr=188308&semester=2010W TISS Seite])

'''LVA Homepage:''' http://ieg.ifs.tuwien.ac.at/~gschwand/teaching/infovis_ue_ws10/index.html

'''Leitung:''' [[Aigner, Wolfgang|Wolfgang Aigner]] [aigner (at) ifs.tuwien.ac.at] 
:: [[Gschwandtner, Theresia|Theresia Gschwandtner]] [gschwandtner (at) ifs.tuwien.ac.at] 

== Gruppen ==

*[[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 01|Gruppe 01 (Emrich, ???, ???)]]
*[[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05|Gruppe 05 (Alili, Bachhuber, Marschik)]]

== News / Bemerkungen ==

Liebe TeilnehmerInnen! 
Um diese Seite einheitlich zu gestalten (auch bezüglich der Vorjahre), schlage ich vor die Nachnamen
der Gruppenmitglieder in Klammer neben der Gruppe anzugeben, 
z.B.: Gruppe XX (Maier, Müller, Mustermann). 
-- [[Gschwandtner, Theresia|Theresia Gschwandtner]] 10:34, 08 October 2010 (CEST)

User:UE-InfoVis1011 0625039

2010-10-18T16:49:03Z

UE-InfoVis1011 0625039: fixed link yet again

<big>'''Patrick Marschik'''</big>, BSc 

[[Image:pm_portrait.jpg|right|Patrick Marschik]]

== Affiliations ==

* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05|Gruppe 05 (Alili, Bachhuber, Marschik)]]
* [http://www.tuwien.ac.at Vienna University of Technology]
* [http://sat.researchstudio.at/people/patrick_marschik_en.html Researchstudio Austria - Smart Agent Technologies]

=== Current Project(s) ===

[http://www.easyrec.org EasyRec]

[[Category:Persons]]

Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05

2010-10-18T16:46:54Z

UE-InfoVis1011 0625039: Created page

Gruppenmitglieder:
* [[User:UE-InfoVis1011_0625039|Marschik, Patrick]]
* Alili, Jasin
* Bachhuber, Ben

Aufgaben
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 1|Aufgabe 1]]
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 2|Aufgabe 2]]
* [[Teaching:TUW - UE InfoVis WS 2010/11 - Gruppe 05 - Aufgabe 3|Aufgabe 3]]