|
|
| (57 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| == Pargnostics: Screen-Space Metrics for Parallel Coordinates ==
| | You've hit the ball out the park! Icnrdeible! |
| | |
| === 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 ''x<sub>i,j</sub>'' 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(h<sup>4</sup>)''.
| |
| 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 ===
| |
| 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 ===
| |
| | |
| === Branch-and-Bound 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
| |