Teaching:TUW - UE InfoVis WS 2006/07 - Gruppe 03 - Aufgabe 1 - Data Density

Definition

Data Density means the number of data points per area of the graph (that is the number of pixels in the display where number of pixels does not include the pixels in the window borders, menus, etc.).

[Brath, 1997]

Number of Data Points means the number of discrete data values represented on screen at an instant.

[Barth, 1997]

Charts and Graphs

While the human eye has the ability to detect large amounts of information within a small area, statistical graphs often fail to take advantage of this ability. To messure the information content of a graph he definses the data density. [Hunt and Mashhoudy, 2002] Therefor you need numerical values which relate the number of maximal at the same time presentable information elements to a display panel. [Edlinger, 2006]

Data density is also used to compute the cognitive complexity. [Edlinger, 2006] To do this you additonaly need the number of dimensions. [Dal Sasso Freitas, 2002]

In "The Visual Display of Graphical Information" of Edward Tufte, a milestone in the theory of graph design, principles of graph design are discussed. One of them is: Try to maximise the data density. [Hunt and Mashhoudy, 2002] and the size of the data matrix, within reason. As the volume of data increases, data measures must shrink and the graphics can be shrunk way down. [Tufte, 1999]

Usually there is a minimum amount, which should always be less than the data density. If the data density falls below this value 0 is used as a result, otherwise 1. [Edlinger, 2006]

The maximum known density for a graph is 110,000 numbers/sq-inch for an astronomical graph. To compare, for most scientific journals we get about 50-200 numbers/sq-inch. [Smith, 2005]

Example for data densities include:

• 150 Mbits = human eye
• 8 Mbits = typical computer screen
• 25 Mbits = color slide
• 150 Mbits = large foldout map
• 28,000 Characters = Reference book
• 18,000 Characters = phone book
• 15,000 Characters = non-fiction

[Smith, 2005]

Example

To better undrestand this term, we show two graphs and compute their data density. Consider the result of a survey in which the gender, height and weight were recordet for 92 students. The charts are 5.6cm by 7.4cm, an area of 41.4cm2. [Hunt and Mashhoudy, 2002]

Above you see a bar graph showing the breakdown into males and females. According the definition you've 2 (female and male) areas with 2 kind of information (gender and number of students), what makes 4 data points. By deviding this over the size of its area, you get the data tensity of this graph. [Barth, 1997]

number of data points = 4

data density = 4 / 41.4 = 0.1 (to 1 dp) [Hunt and Mashhoudy, 2002]

The computation of the second example works similiar to the first one. The second graph shows a labelled XY-chart, which additonaly shows the relationship between height and weight of the students. As a result you've 3 kind of information on 92 areas, what results 276 data points. [Barth, 1997]

number of data points = 92 x 3 = 276

data density = 276 / 41.4 = 6.7 (to 1 dp) [Hunt and Mashhoudy, 2002]

References

[Barth, 1997] R. Barth. Metrics for effective information visualization. In Proceedings of the 1997 IEEE Symposium on Information Visualization (InfoVis '97), pages 0–108, DC, USA, October 1997. IEEE Computer Society Washington

[Dal Sasso Freitas et al., 2002] Carla M. Dal Sasso Freitas, Paulo R. G. Luzzardi, Ricardo A. Cava, Marco A. A. Winckler, Marcelo S. Pimenta, Luciana P. Nedel. Evaluating Usability of Information Visualization Techniques. In Proceedings of 5th Symposium on Human Factors in Computer Systems (IHC), pages 10-11, Fortaleza, CE, 2002. Fortaleza:SBC

[Edlinger, 2006] Karl Edlinger, Informationsvisualisierung im Wissensmanagement – Eine Analyse unterschiedlicher Visualisierungstechniken auf ihre Eignung für das Wissensmanagement, Master's thesis, Fachhochschul-Studiengang Informationsberufe, Eisenstadt, 2006, 31-32.

[Hunt and Mashhoudy, 2002] Neville Hunt and Housh Mashhoudy, Discovering Important Statistical Concepts Using SpreadSheets. Created at: January 29, 2002. Retrieved at: October 28, 2006. http://home.ched.coventry.ac.uk/Volume/vol0/philosop.htm.

[Smith, 2005] Waynes Smith, Graphics and Web Design Based on Edward Tufte's Principles. Created at: January 17, 2005. Retrieved at: October 29, 2006. http://www.washington.edu/computing/training/560/zz-tufte.html

[Tufte, 1999] Edward R. Tufte, The Visual Display of Quantitative Information. Created at: January 26, 1999. Retrieved at: October 29, 2006. http://ldt.stanford.edu/ldt1999/Students/mizuno/Portfolio/Work/reports/tufte/ed229c-tufte-outline.html