“Exploring High-D Spaces with Multiform
Matrices and Small Multiples”
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/
Mudit Agrawal
Nathaniel Ayewah
The Plan





Motivation
Contribution
Analysis Methods
GeoVISTA studio
Conclusions
Motivation

Discover Multivariate relationships

Examine data from multiple perspectives
DATA  INFORMATION
Contribution

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

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
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
Sorting

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
Source: (Siirtola, 1999)
Analysis Methods
Space-filling visualization
Mosaic plot
Sunburst methods
Source: (Schedl, 2006)
Source: (Young, 1999)
Pixel-oriented methods
Source: (Keim, 1996)
Analysis Methods
Multiform Bivariate Small Multiple

Small Multiples
A set of juxtaposed data
representations that together
support understanding of
multivariate information
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
1
mean
1
2
mean
2
3
4
Source: (Guo, 2003)
Conditional Entropy
Source: (Guo, 2003)
Ordering Dimensions

Related dimensions should be close together
Sort By: Conditional Entropy
A
A
B
5
B
5
C
16 15
D
9
C
16
D
9
Sort Method: Minimum Spanning Tree
5
A
9
B
15
16
21
15 21
21
4
C
4
D
4
unsorted
Ordering: B A D C
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.