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| = Pargnostics: Screen-Space Metrics for Parallel Coordinates =
| | You've hit the ball out the park! Icnrdeible! |
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| == Introduction ==
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| Visualization still takes place in a space with a limited number of discrete
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| pixels. The result of this often is over-plotting, clutter or other things.
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| 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.
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| Until know not a lot of attention is paid to the way visualzation is presented on the screen.
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| 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.
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| Based on metrics it's possible to provide an optimization which maximize or minimize certain visual artifacts.
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| == Metrics ==
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| [[Image:Dasgupta+Kosara Pixel-Space Histograms.png|thumb|300px|right|Figure 1: Pixel-space histograms, see [Dasgupta and Kosara, 2010] p1018]]
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| To automatically enhance the analytical tasks of users Dasgupta and Kosara [2010] proposed several metrics.
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| The metrics are used to measure the properties of parallel coordinates.
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| For calculating these metrics, first ''pixel-space histograms'' need to be calculated.
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| 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):
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| * ''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.
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| * ''One-Dimensional Distance Histogram'': A vector ''d'' where each component measures the slope of lines.
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| * ''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.
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| 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).
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| === Number of Line Crossings ===
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| The first metric proposed by Dasgupta and Kosara [2010] is ''number of line crossings''.
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| This intuitively just does what the name implies, count how many line crossings there are between two axes of the prallel coordinates.
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| The count is efficiently calculated by using intervals as proposed by [Allen, 1983; Rit 1986] with a complexity of ''O(h<sup>4</sup>)''.
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| This count is then normalized by the maximum number of possible crossings in order compare the metric between different axis combinations.
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| === Angles of Crossing ===
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| === Parallelism ===
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| === Mutual Information ===
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| === Convergence, Divergence ===
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| === Over-plotting ===
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| === Pixel-based Entropy ===
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| == Dimension Order Optimization ==
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| == Conclusion ==
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| == References ==
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| *[Allen, 1983] J. Allen. Maintaining knowledge about temporal intervals. ''Communications of the ACM'', 26:832-843, 1983.
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| *[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.
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| *[Rit, 1986] J.-F. Rit. Propagating temporal constraints for scheduling. In ''Proceedings of the Fifth National COnference on Artificial Intelligence'', pages 383-388, 1986
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