Quality Metrics for Visual Analytics of High-Dimensional Data

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Quality Metrics for Visual Analytics of High-Dimensional Data Daniel A. Keim Data Analysis and Information Visualization Group University of Konstanz, Germany Workshop on Visual Analytics and Information Fusion at KDD 2011 August 21, 2011 Definition of Visual Analytics Definition: Visual Analytics is the science of analytical reasoning facilitated by visual interfaces. Visual analytics techniques are needed to integrate data from massive, dynamic, ambiguous, and often conflicting sources analyze the data to derive new insights make critical decisions in real-time. 1

Definition of Visual Analytics Visual Analytics: Tight Integration of Visual and Automatic Data Analysis Methods for Information Exploration and Scalable Decision Support Visual Data Exploration Visualisation Data Knowledge Models Automated Data Analysis Feedback loop Roadmap from the VisMaster EU Project www.visual-analytics.eu 2

Technical Challenges When should we use automated techniques versus interactive ti techniques? When do we need both? How to best combine interactive visualizations with automated t analysis techniques? The KDD Pipeline Fayyad, U. M. et al. 1996. From data mining to knowledge discovery: an overview. In Fayyad, U. M.et al (Eds.), Advances in knowledge discovery and data mining. AAAI Press / The MIT Press. 3

Quality-Metrics-Driven Automation Enrico Bertini, Member, Andrada Tatu, Daniel Keim: Quality Metrics in High-Dimensional Data Visualization: An Overview and Systematization, IEEE Conf. on Information Visualization, 2011. Outline Visual Analytics Definition Challenges Quality Metrics Quality Metrics for Visual Mappings Data Transformations View Transformations Perspectives 4

Quality Metrics for Visual Mapping Automated Mapping Support for Pixel Bar Charts for Scatter Plots for Parallel Coordinates Pixel Bar Charts Equal-Width Pixel Bar Chart D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. 5

Pixel Bar Charts Product Type Product Type Equal-Height Pixel Bar Chart D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. Pixel Bar Charts high low 1 23 4 5 6 7 10 11 12 1 23 4 5 6 7 1011 11 12 1 23 4 5 6 7 1011 11 12 Product Type Product Type Product Type Color=dollar amount Color=number of visits Color=quantity Multi Pixel Bar Charts D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. 6

Pixel Bar Charts A pixel bar chart is defined by a five tuple <D x, D y, O x, O y, C> where D x, D y, O x, O y, C {A l,, A k, } and D x / D y are the dividing attributes on the x-/y-axes O x / O y are the ordering attributes on the x-/y-axes C defines the coloring attribute(s) D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. Pixel Bar Charts Dividing Attribute on x-axis (e.g. Product Type) D x D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. 7

Pixel Bar Charts D y Dividing Attribute on y-axis (e.g. Region) D x D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. Pixel Bar Charts C O y O x Ordering Attributes on x- and y-axes D. A. Keim, M. C. Hao, U. Dayal and M. Hsu. Pixel Bar Charts: A Visualization Technique for Very Large Multi-Attribute Data Sets. Visualization, San Diego 2001, extended version in: Information Visualization Journal, Palgrave, 1 (2), 2002. 8

Automated Mapping Support for Pixel Bar Charts Data Parameter Setting Visualization Color = Blocknumber D x PixelBarCharts Rework Fail Pass Color = Wert OT O y Color = Wert BKSL O x min max Parameter Space Very Large Interactive Exploration impossible Automated Mapping Support for Pixel Bar Charts Candidate Set P 1,,P n Relevance feedback J. Schneidewind, M. Sips and D. A. Keim. Pixnostics: Towards Measuring the Value of Visualization. In Proceedings of the IEEE Symposium on Visual Analytics Science and Technology (VAST '06), 2006. 9

Automated Mapping Support for Pixel Bar Charts 900 Pixel Bar Charts only few provide insight J. Schneidewind, M. Sips and D. A. Keim. Pixnostics: Towards Measuring the Value of Visualization. In Proceedings of the IEEE Symposium on Visual Analytics Science and Technology (VAST '06), 2006. Automated Mapping Support for Pixel Bar Charts Rework Fail Pass ID Temperature SSL Detailed analysis of attribute combinations: The 2nd bar reveals an obvious pattern 25 most relevant Pixel Bar Charts constructed from highly ranked attribute combinations (Correlation Analysis / Classification) J. Schneidewind, M. Sips and D. A. Keim. Pixnostics: Towards Measuring the Value of Visualization. In Proceedings of the IEEE Symposium on Visual Analytics Science and Technology (VAST '06), 2006. 10

Automated Mapping Support for Pixel Bar Charts after sorting according to our measure J. Schneidewind, M. Sips and D. A. Keim. Pixnostics: Towards Measuring the Value of Visualization. In Proceedings of the IEEE Symposium on Visual Analytics Science and Technology (VAST '06), 2006. Automated Mapping Support?? 11

Automated Mapping Support for Scatter Plots Scatterplots with class information Each color represents one class Evaluate scatterplots according their separation properties Algorithm: Separate classes in distinct images Compute a density image for each one Estimate the mutual overlap Automated Mapping Support for Scatter Plots Best ranked views Olives dataset (Class Density Measure) Worst ranked views 12

Rotating Variance Measure Find linear and non-linear correlations between pairwise dimensions Continuous density field Local density for each pixel p: ρ = 1/r r = enclosing sphere of the k-nearest neighbors of p Rotating Variance Measure Take samples along different lines centered at the corresponding pixel. Compute the weighted distribution for each pixel x i Compute the weighted distribution for each pixel x 13

Rotating Variance Measure For each column y in the image we compute the minimum v i value and sum up the result, where v(x,y) = v i Automated Mapping Support for Scatter Plots Parkinson s disease dataset (Rotating Variance Measure) Best ranked views Worst ranked views 14

Hough Space Measure Interesting patterns are usually clustered lines with similar positions and directions Hough Transform y = ax + b b= - ax + y Problem: the slope of vertical lines is infinite Normal representation: ρ = xcosθ + ysinθ y ρ x θ Hough Space Measure For each non-background pixel in the visualization, we have a distinct sinusoidal curve in the ρθ-plane Hough/Accumulator Space Hough/Accumulator Space y ρ y ρ x θ x θ 15

Hough Space Measure Good visualizations must contain fewer well defined clusters, i.e. accumulator cells with high values Compute the median value m as an adaptive threshold s i, j 1 # # highvaluecells #Cells Hough Space Measure Overall quality measure Exhaustively computing all n-dimensions combinations Long computation time Unfeasible for a large n Solve a Traveling Salesman Problem A*-Search algorithm 16

Automated Mapping Support for Parallel Coordinates Parkinson s disease dataset (Hough Space Measure) Best ranked views Worst ranked views Automated Mapping Support for Parallel Coordinates Cars dataset (Hough Space Measure for all Classes) Best ranked views Worst ranked views 17

Outline Visual Analytics Definition Challenges Quality Metrics Quality Metrics for Visual Mappings Data Transformations View Transformations Perspectives Quality Metrics for Data Transformation Quality Metrics for Filtering Jing Yang,Wei Peng, Matthew O. Ward and Elke A. Rundensteiner: Interactive Hierarchical Dimension Ordering, Spacing and Filtering for Exploration of High Dimensional Datasets, IEEE Symposium on Information Visualization 2003 (InfoVis 2003), pp 105-112, 2003. 18

Quality Metrics for Data Transformation Quality Metrics for Sorting Dimensions S. Johansson and J. Johansson: Interactive Dimensionality Reduction Through User-defined Combinations of Quality Metrics, IEEE Trans. On Visualization and Computer Graphics, 2009. Outline Visual Analytics Definition Challenges Quality Metrics Quality Metrics for Visual Mappings Data Transformations View Transformations Perspectives 19

Quality Metrics for View Transformation Metrics for View Distortion Jing Yang,Wei Peng, Matthew O. Ward and Elke A. Rundensteiner: Interactive Hierarchical Dimension Ordering, Spacing and Filtering for Exploration of High Dimensional Datasets, IEEE Symposium on Information Visualization 2003 (InfoVis 2003), pp 105-112, 2003. Outline Visual Analytics Definition Challenges Quality Metrics Quality Metrics for Visual Mappings Data Transformations View Transformations Perspectives 20

Enrico Bertini, Member, Andrada Tatu, Daniel Keim: Quality Metrics in High-Dimensional Data Visualization: An Overview and Systematization, IEEE Conf. on Information Visualization, 2011. Outline Visual Analytics Definition Challenges Quality Metrics Quality Metrics for Visual Mappings Data Transformations View Transformations Perspectives 21

Pipelines Visual Analytics Data Data Data Visualization of the data DM-Algorithm Result Visualization of the DM-Algorithm result Result Visualization of the result DM-Algorithm step 1 DM-Algorithm step n Result Visualization + Interaction Knowledge Knowledge Knowledge Preceding Visualization Subsequent Visualization Visual Analytics 22

Conclusion All truths are easy to understand once they are discovered; the point is to discover them. Galileo Galile (1564-1642) Questions? infovis.uni-konstanz.de www.idvbook.com Advanced Visual Analytics Interfaces - AVI 2010 23

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