UC Berkeley, 09/19/00 An Introduction to Multivariate Data Visualization and XmdvTool Matthew O. Ward Computer Science Department Worcester Polytechnic Institute This work was supported under NSF Grant IIS

UC Berkeley, 09/19/00 What is Multivariate Data? zEach data point has N variables or observations zEach observation can be: y nominal or ordinal ydiscrete or continuous yscalar, vector, or tensor zMay or may not have spatial, temporal, or other connectivity attribute

UC Berkeley, 09/19/00 Characteristics of a Variable zOrder: grades have an order, brand names do not. zDistance metric: for income, distance equals difference. For rankings, difference is not a distance metric. zAbsolute zero: temperature has an absolute zero, bank account balances do not. zA variable can be classified by these three attributes, called Scale. zEffective visualizations attempt to match the scale of the data dimension with the graphical attribute conveying it.

UC Berkeley, 09/19/00 Sources of Multivariate Data zSensors (e.g., images, gauges) zSimulations zCensus or other surveys zCommerce (e.g., stock market) zCommunication systems zSpreadsheets and databases

UC Berkeley, 09/19/00 Issues in Visualizing Multivariate Data zHow many variables? zHow many records? zTypes of variables? zUser task (exploration, confirmation, presentation) zData feature of interest (clusters, anomalies, trends, patterns, ….) zBackground of user (domain expert, visualization specialist, decision-maker, ….)

UC Berkeley, 09/19/00 Methods for Visualizing Multivariate Data zDimensional Subsetting zDimensional Reorganization zDimensional Embedding zDimensional Reduction

UC Berkeley, 09/19/00 Dimensional Subsetting zScatterplot matrix displays all pairwise plots zSelection allows linkage between views zClusters, trends, and correlations readily discerned between pairs of dimensions

UC Berkeley, 09/19/00 Dimensional Reorganization zParallel Coordinates creates parallel, rather than orthogonal, dimensions. zData point corresponds to polyline across axes zClusters, trends, and anomalies discernable as groupings or outliers, based on intercepts and slopes

UC Berkeley, 09/19/00 Dimensional Reorganization (2) zGlyphs map data dimensions to graphical attributes zSize, color, shape, and orientation are commonly used zSimilarities/differences in features give insights into relations

UC Berkeley, 09/19/00 Dimensional Embedding zDimensional stacking divides data space into bins zEach N-D bin has a unique 2-D screen bin zScreen space recursively divided based on bin count for each dimension zClusters and trends manifested as repeated patterns

UC Berkeley, 09/19/00 Dimensional Reduction zMap N-D locations to M-D display space while best preserving N-D relations zApproaches include MDS, PCA, and Kohonen Self Organizing Maps zRelationships conveyed by position, links, color, shape, size, etc.

UC Berkeley, 09/19/00 The Role of Selection zUser needs to interact with display, examine interesting patterns or anomalies, validate hypotheses zSelection allows isolation of subset of data for highlighting, deleting, focussed analysis zDirect (clicking on displayed items ) vs. indirect (range sliders) zScreen space (2-D) vs. data space (N-D)

UC Berkeley, 09/19/00 Demonstration of XmdvTool

UC Berkeley, 09/19/00 Problems with Large Data Sets zMost techniques are effective with small to moderate sized data sets zLarge sets (> 50K records) are increasingly common zWhen traditional visualizations used, occlusion and clutter make interpretation difficult

UC Berkeley, 09/19/00 One Potential Solution zMultiresolution displays with aggregation zExplicit clustering yBreak dimensions into bins yAggregate in a particular order (datacubes) zImplicit clustering yHierarchical clustering (proximity-based merging) yHierarchical partitioning (proximity-based splits) zProblem: many ways to cluster, each revealing different aspects of data

UC Berkeley, 09/19/00 Display Options zFor each cluster, show yCenter yExtents for each dimension yPopulation yOther descriptors (e.g., quartiles) zColor clusters such that siblings have similar color to parents

UC Berkeley, 09/19/00 Hierarchical Parallel Coordinates zBands show cluster extents in each dimension zOpacity conveys cluster population zColor similarity indicates proximity in hierarchy

UC Berkeley, 09/19/00 Hierarchical Scatterplots zClusters displayed as rectangles, showing extents in 2 dimensions zColor/opacity consistently used for relational and population info

UC Berkeley, 09/19/00 Hierarchical Glyphs zStar glyph with bands zAnalogous to parallel coordinates, with radial rather than parallel dimensions zGlyph position critical for conveying relational info

UC Berkeley, 09/19/00 Hierarchical Dimensional Stacking zClusters occupy multiple bins zOverlaps can be reduced by increasing number of bins zCell colors can be blended, or display last cluster mapped to space

UC Berkeley, 09/19/00 Hierarchical Star Fields zDimensional reduction techniques commonly displayed with starfields zEach cluster becomes circle/sphere in field zAlternatively, can show glyph at cluster location

UC Berkeley, 09/19/00 Navigating Hierarchies zDrill-down, roll-up operations for more or less detail zNeed selection operation to identify subtrees for exploration, pruning zNeed indications of where you are in hierarchy, and where you’ve been during exploration process

UC Berkeley, 09/19/00 Structure-Based Brushing zEnhancement to screen-based and data- based methods zSpecify focus, extents, and level of detail zIntuitive - wedge of tree and depth of interest zImplemented by labeling/numbering terminals and propagating ranges to parents

UC Berkeley, 09/19/00 Structure-Based Brush zWhite contour links terminal nodes zRed wedge is extents selection zColor curve is depth specification zColor bar maps location in tree to unique color zDirect and indirect manipulation of brush

UC Berkeley, 09/19/00 Demonstration of Hierarchical Features in XmdvTool

UC Berkeley, 09/19/00 Auxiliary Tools zExtent scaling to reduce occlusion of bands zDimensional zooming - fill display with selected subspace (N-D distortion) zDynamic masking to fade out selected or unselected data zSaving selected subsets zEnabling/disabling dimensions zUnivariate displays (Tukey box plots, tree maps)

UC Berkeley, 09/19/00 Summary zMany ways to map multivariate data to images, each with strengths and weaknesses zLinking between and within displays with brushing enhances static displays and combines their strengths. zHierarchies and aggregations allow visualization of large data sets zIntuitive navigation, filtering, and focus critical to exploration process zEach basic multivariate visualization method is readily extensible to displaying cluster information

UC Berkeley, 09/19/00 Problems and Future Work zMany data characteristics not currently supported (e.g., text fields, records with missing entries, data quality) zNavigation tool for hierarchies assumes linear order of nodes yLooking at tools for dynamic reorganization yExploring 2-D or higher navigation interfaces zVery large hierarchies are difficult to focus on a narrow subset yDeveloping multiresolution interface yInvestigating distortion techniques for navigation

UC Berkeley, 09/19/00 Other Future Work zProjection pursuit or view recommender zLinking structure and data brushing zUser studies zCustomization based on domain zQuery optimization via caching and prefetching

UC Berkeley, 09/19/00 For More Information zXmdvTool available to the public domain zBoth Unix and Windows support zNext release will have Oracle interface, with query optimization to support exploratory operations zhttp://davis.wpi.edu/~xmdv zPapers in Vis ‘94, ‘95, ‘99, Infovis ‘99, IEEE TVCG Vol. 6, No. 2, 2000

UC Berkeley, 09/19/00 Thanks to….. zElke Rundensteiner zYing-Huey Fua zDaniel Stroe zYang Jing zSuggestions from Xmdv users zNSF