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Importance-Driven Time-Varying Data Visualization Chaoli Wang, Hongfeng Yu, Kwan-Liu Ma University of California, Davis. Importance-Driven Volume Rendering. [Viola et al. 04]. Differences. Medical or anatomical data sets Pre-segmented objects Importance assignment Focus on rendering
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Importance-Driven Time-Varying Data VisualizationChaoli Wang, Hongfeng Yu, Kwan-Liu MaUniversity of California, Davis
Importance-Driven Volume Rendering [Viola et al. 04]
Differences • Medical or anatomical data sets • Pre-segmented objects • Importance assignment • Focus on rendering • Time-varying scientific data sets • No segmentation or objects are given • Importance measurement • Focus on data analysis
Questions • How to capture the important aspect of data? • Importance – amount of change, or “unusualness” • How to utilize the importance measure? • Data classification • Abnormality detection • Time budget allocation • Time step selection
Related Work • Time-varying data visualization • Spatial and temporal coherence [Shen et al. 94, Westermann 95, Shen et al. 99] • Compression, rendering, presentation [Guthe et al. 02, Lum et al. 02, Woodring et al. 03] • Transfer function specification [Jankun-Kelly et al. 01, Akiba et al. 06] • Time-activity curve (TAC) [Fang et al. 07] • Local statistical complexity (LSC) [Jänicke et al. 07]
Importance Analysis • Block-wise approach • Importance evaluation • Amount of information a block contains by itself • New information w.r.t. other blocks in the time series • Information theory • Entropy • Mutual information • Conditional entropy
Information Theory • Entropy • Mutual information • Conditional entropy p(x), p(y): Marginal probability distribution function p(x,y): Joint probability distribution function
Relations with Venn Diagram H(X) H(Y) I(X;Y) H(X|Y) H(Y|X) I(X;Y) = I(Y;X) H(X|Y) ≠H(Y|X)
Entropy in Multidimensional Feature Space f3 • Feature vector • Data value • Gradient magnitude or other derivatives • Domain-specific quantities • Multidimensional histogram • Use the normalized bin count as probability p(x) f2 f1
Importance in Joint Feature-Temporal Space F • Consider two data blocks X and Y at • the same spatial location • neighboring time steps • Use joint feature-temporal histogram • Use the normalized bin count as probability p(x,y) • Run-length encode the histogram F = (f1, f2, f3, …) F
Importance Value Calculation • Consider a time window for neighboring blocks • Importance of a data block Xj at time step t: • Importance of time step t:
I T Importance Curve – Earthquake Data Set regular
I T Importance Curve – Climate Data Set periodic
I T Importance Curve – Vortex Data Set turbulent
Clustering Importance Curves • Hybrid k-means clustering [Kanungo et al. 02] • Lloyd’s algorithm • Local search by swapping centroids • Avoid getting trapped in local minima
Clustering All Time Steps vs. Time Segments 599 time steps 50 segments 1200 time steps 120 segments 90 time steps 90 segments
Abnormality Detection A: El Niño B: La Niña
Time Budget Allocation • Allocate time budget based on importance value • Animation time • Non-even allocation • Rendering time • Assign to each time step (and each block in a time step) • Adjust the sampling spacing accordingly
Time Step Selection • Uniform selection • Importance-driven selection • Select the first time step • Partition the rest of time steps into (K-1) segments • In each time segment, select one time step: • Maximize the joint entropy
Precomputation and Clustering Performance • The test data sets with their parameter settings, sizes of joint feature-temporal histograms, and timings for histogram calculation. • Timing for clustering all time steps of the five test data sets.
Choices of Window and Bin Sizes • The importance curve of the vortex data set with different time window sizes (W) and numbers of bins for feature components F = (f1, f2, f3).
3 clusters 4 clusters 5 clusters 50×50×20 20×20×20 10×10×20 Choices of # of Clusters and Block Size • The cluster of the highest importance values under different choices of number of clusters and block size. Top row: color adjustment only. Bottom row: color and opacity adjustment.
Artifact Along Block Boundaries 20×20×20 10×10×20
Summary • Importance-driven data analysis and visualization • Quantify data importance using conditional entropy • Cluster the importance curves • Leverage the importance in visualization • Limitations • Block-based classification • Size of joint feature-temporal histogram • Extensions • Non-uniform data partition • Incorporate domain knowledge • Dimension reduction
Acknowledgements • NSF • CCF-0634913, CNS- 0551727, OCI-0325934, OCI-0749227, and OCI-0749217 • DOE SciDAC Program • DE-FC02-06ER25777, DE-FG02-08ER54956, and DE-FG02-05ER54817 • Data sets • Combustion: Jacqueline H. Chen, SNL • Climate: Andrew T. Wittenberg, NOAA • Earthquake: CMU quake group • Hurricane: NSF, IEEE Visualization 2004 Contest