An Introduction to Multivariate Data Visualization and XmdvTool

1
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-9732897
2
What is Multivariate Data?

• Each data point has N variables or observations
• Each observation can be
• nominal or ordinal
• discrete or continuous
• scalar, vector, or tensor
• May or may not have spatial, temporal, or other
  connectivity attribute

3
Characteristics of a Variable

• Order grades have an order, brand names do not.
• Distance metric for income, distance equals
  difference. For rankings, difference is not a
  distance metric.
• Absolute zero temperature has an absolute zero,
  bank account balances do not.
• A variable can be classified by these three
  attributes, called Scale.
• Effective visualizations attempt to match the
  scale of the data dimension with the graphical
  attribute conveying it.

4
Sources of Multivariate Data

• Sensors (e.g., images, gauges)
• Simulations
• Census or other surveys
• Commerce (e.g., stock market)
• Communication systems
• Spreadsheets and databases

5
Issues in Visualizing Multivariate Data

• How many variables?
• How many records?
• Types of variables?
• User task (exploration, confirmation,
  presentation)
• Data feature of interest (clusters, anomalies,
  trends, patterns, .)
• Background of user (domain expert, visualization
  specialist, decision-maker, .)

6
Methods for Visualizing Multivariate Data

• Dimensional Subsetting
• Dimensional Reorganization
• Dimensional Embedding
• Dimensional Reduction

7
Dimensional Subsetting

• Scatterplot matrix displays all pairwise plots
• Selection allows linkage between views
• Clusters, trends, and correlations readily
  discerned between pairs of dimensions

8
Dimensional Reorganization

• Parallel Coordinates creates parallel, rather
  than orthogonal, dimensions.
• Data point corresponds to polyline across axes
• Clusters, trends, and anomalies discernable as
  groupings or outliers, based on intercepts and
  slopes

9
Dimensional Reorganization (2)

• Glyphs map data dimensions to graphical
  attributes
• Size, color, shape, and orientation are commonly
  used
• Similarities/differences in features give
  insights into relations

10
Dimensional Embedding

• Dimensional stacking divides data space into bins
• Each N-D bin has a unique 2-D screen bin
• Screen space recursively divided based on bin
  count for each dimension
• Clusters and trends manifested as repeated
  patterns

11
Dimensional Reduction

• Map N-D locations to M-D display space while best
  preserving N-D relations
• Approaches include MDS, PCA, and Kohonen Self
  Organizing Maps
• Relationships conveyed by position, links, color,
  shape, size, etc.

12
The Role of Selection

• User needs to interact with display, examine
  interesting patterns or anomalies, validate
  hypotheses
• Selection allows isolation of subset of data for
  highlighting, deleting, focussed analysis
• Direct (clicking on displayed items ) vs.
  indirect (range sliders)
• Screen space (2-D) vs. data space (N-D)

13
Demonstration of XmdvTool
14
Problems with Large Data Sets

• Most techniques are effective with small to
  moderate sized data sets
• Large sets (gt 50K records) are increasingly
  common
• When traditional visualizations used, occlusion
  and clutter make interpretation difficult

15
One Potential Solution

• Multiresolution displays with aggregation
• Explicit clustering
• Break dimensions into bins
• Aggregate in a particular order (datacubes)
• Implicit clustering
• Hierarchical clustering (proximity-based merging)
• Hierarchical partitioning (proximity-based
  splits)
• Problem many ways to cluster, each revealing
  different aspects of data

16
Display Options

• For each cluster, show
• Center
• Extents for each dimension
• Population
• Other descriptors (e.g., quartiles)
• Color clusters such that siblings have similar
  color to parents

17
Hierarchical Parallel Coordinates

• Bands show cluster extents in each dimension
• Opacity conveys cluster population
• Color similarity indicates proximity in hierarchy

18
Hierarchical Scatterplots

• Clusters displayed as rectangles, showing extents
  in 2 dimensions
• Color/opacity consistently used for relational
  and population info

19
Hierarchical Glyphs

• Star glyph with bands
• Analogous to parallel coordinates, with radial
  rather than parallel dimensions
• Glyph position critical for conveying relational
  info

20
Hierarchical Dimensional Stacking

• Clusters occupy multiple bins
• Overlaps can be reduced by increasing number of
  bins
• Cell colors can be blended, or display last
  cluster mapped to space

21
Hierarchical Star Fields

• Dimensional reduction techniques commonly
  displayed with starfields
• Each cluster becomes circle/sphere in field
• Alternatively, can show glyph at cluster location

22
Navigating Hierarchies

• Drill-down, roll-up operations for more or less
  detail
• Need selection operation to identify subtrees for
  exploration, pruning
• Need indications of where you are in hierarchy,
  and where youve been during exploration process

23
Structure-Based Brushing

• Enhancement to screen-based and data-based
  methods
• Specify focus, extents, and level of detail
• Intuitive - wedge of tree and depth of interest
• Implemented by labeling/numbering terminals and
  propagating ranges to parents

24
Structure-Based Brush

• White contour links terminal nodes
• Red wedge is extents selection
• Color curve is depth specification
• Color bar maps location in tree to unique color
• Direct and indirect manipulation of brush

25
Demonstration of Hierarchical Features in XmdvTool
26
Auxiliary Tools

• Extent scaling to reduce occlusion of bands
• Dimensional zooming - fill display with selected
  subspace (N-D distortion)
• Dynamic masking to fade out selected or
  unselected data
• Saving selected subsets
• Enabling/disabling dimensions
• Univariate displays (Tukey box plots, tree maps)

27
Summary

• Many ways to map multivariate data to images,
  each with strengths and weaknesses
• Linking between and within displays with brushing
  enhances static displays and combines their
  strengths.
• Hierarchies and aggregations allow visualization
  of large data sets
• Intuitive navigation, filtering, and focus
  critical to exploration process
• Each basic multivariate visualization method is
  readily extensible to displaying cluster
  information

28
Problems and Future Work

• Many data characteristics not currently supported
  (e.g., text fields, records with missing entries,
  data quality)
• Navigation tool for hierarchies assumes linear
  order of nodes
• Looking at tools for dynamic reorganization
• Exploring 2-D or higher navigation interfaces
• Very large hierarchies are difficult to focus on
  a narrow subset
• Developing multiresolution interface
• Investigating distortion techniques for navigation

29
Other Future Work

• Projection pursuit or view recommender
• Linking structure and data brushing
• User studies
• Customization based on domain
• Query optimization via caching and prefetching

30
For More Information

• XmdvTool available to the public domain
• Both Unix and Windows support
• Next release will have Oracle interface, with
  query optimization to support exploratory
  operations
• http//davis.wpi.edu/xmdv
• Papers in Vis 94, 95, 99, Infovis 99, IEEE
  TVCG Vol. 6, No. 2, 2000

31
Thanks to..

• Elke Rundensteiner
• Ying-Huey Fua
• Daniel Stroe
• Yang Jing
• Suggestions from Xmdv users
• NSF