1. Multivariate Data Visualization Adapted from Slides by: Matthew O. Ward Computer Science Department Worcester Polytechnic Institute This work was supported under NSF Grant IIS-9732897

2. 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

3. 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. 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.

4. Sources of Multivariate Data zSensors (e.g., images, gauges) zSimulations zCensus or other surveys zCommerce (e.g., stock market) zCommunication systems zSpreadsheets and databases

5. 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, ….)

6. Methods for Visualizing Multivariate Data zDimensional Subsetting zDimensional Reorganization zDimensional Reduction

7. Dimensional Subsetting zScatterplot matrix displays all pairwise plots zSelection allows linkage between views zClusters, trends, and correlations readily discerned between pairs of dimensions

8. 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

9. Dimensional Reorganization zGlyphs map data dimensions to graphical attributes zSize, color, shape, and orientation are commonly used zSimilarities/differences in features give insights into relations

10. 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.

11. 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)

12. 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)