“Exploring High-D Spaces with Multiform Matrices and Small Multiples”

Mudit Agrawal

Nathaniel Ayewah

MacEachren, A., Dai, X., Hardisty, F., Guo, D., and Lengerich, G.Proc. IEEE Symposium on Information Visualization (2003), 31–38.

http://www.geovista.psu.edu/

The Plan

Motivation Contribution Analysis Methods GeoVISTA studio Conclusions

Discover Multivariate relationships

Examine data from multiple perspectives

Motivation

DATA INFORMATION

Visual analysis of multivariate data

Combinations of scatterplots, bivariate maps and space-filling displays

Conditional Entropy to identify interesting variables from a data-set, and to order the variables to show more information

Dynamic query/filtering called Conditioning

Contribution

Contribution

Back-end: Design Box Building of applications using visual programming tools

Front-end: GUI Box Visualizing data using the developed designs

Source: GeoVista Studio

Analysis Methods

Sorting Nested sorting – sort a table on selected attributes

To understand the relationships between sorted variables and the rest

Permutation Matrix : cell values are replaced by graphical depiction of value. Rows/cols can be sorted to search for related entities e.g.

Analysis Methods

Augmented seriation: Organizing a set of objects along a single dimension

using multimodal multimedia

Correlation matrices

Reorderable Matrices: Simple interactive

visualization artifact for tabular data

Analysis Methods

Sorting

Source: (Siirtola, 1999)

Space-filling visualization

Analysis Methods

Sunburst methodsMosaic plot

Pixel-oriented methods

Source: (Keim, 1996)

Source: (Schedl, 2006)Source: (Young, 1999)

Multiform Bivariate Small Multiple

Small Multiples A set of juxtaposed data representations that together support understanding of multivariate information

Analysis Methods

Source: (MacEachren, 2003)

Analysis Methods

Multiform Bivariate Matrix

Source: (MacEachren, 2003)

GeoVista Studio

Demonstration

Basic Demo Application construction Scatterplot, Geomap Dynamic linking, eccentric labeling etc.

Dealing with High Dimensionality

High Dimensionality

Interactive Feature Selection Guo, D., 2003. Coordinating Computational and Visualization

Approaches for Interactive Feature Selection and Mulivariate Clustering. Information Visualization 2(4): 232-246.

High Dimensionality

“Goodness of Clustering” high coverage high density high dependence

E.g. Correlation Chi-squared Conditional Entropy

HIGH

HIGH

LOW

Conditional Entropy

Discretize two dimensions into intervals Nested Means

mean

mean mean

1 2

1 2 3 4

Source: (Guo, 2003)

Conditional Entropy

Source: (Guo, 2003)

Ordering Dimensions

Related dimensions should be close together

Sort By: Conditional Entropy Sort Method: Minimum Spanning Tree

A B C D

A 5 16 9

B 5 15 21

C 16 15 4

D 9 21 4

A B

C D

16

5

4

21159

Ordering: B A D Cunsorted

Demonstration

Advanced Demo Interactive Feature Selection PCP, SOM, Matrix Conditioning

Conclusions

Strengths Dynamic Linking of different representations Visualizing clusters of dimensions Rich and extensible toolbox

Weaknesses Usability Arrangement of Windows

References Guo, D., (2003). Coordinating Computational and Visualization Approaches

for Interactive Feature Selection and Mulivariate Clustering. Information Visualization 2(4): 232-246.

Keim, D (1996) Pixel-oriented Visualization Techniques for Exploring Very Large Databases, Journal of Computational and Graphical Statistics.

Schedl, M (2006), CoMIRVA: Collection of Music Information Retrieval and Visualization Applications. Website. http://www.cp.jku.at/people/schedl/Research/Development/CoMIRVA/webpage/CoMIRVA.html

Siirtola, H. (1999), Interaction with the Reorderable Matrix. In E. Banissi, F. Khosrowshahi, M. Sarfraz, E. Tatham, and A. Ursyn, editors, Information Visualization IV '99, pages 272-277. Proceedings International Conference on Information Visualization.

Young, F (1999), Frequency Distribution Graphs (Visualizations) for Category Variables, unpublished. http://forrest.psych.unc.edu/research/vista-frames/help/lecturenotes/lecture02/repvis4a.html .