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

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“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

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### “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
• 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

Sorting

Analysis Methods

• 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.
Sorting

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

Source: (Siirtola, 1999)

Space-filling visualization

Analysis Methods

Mosaic plot

Sunburst methods

Source: (Schedl, 2006)

Source: (Young, 1999)

Pixel-oriented methods

Source: (Keim, 1996)

Multiform Bivariate Small Multiple

Analysis Methods

• Small Multiples

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

Source: (MacEachren, 2003)

Multiform Bivariate Matrix

Analysis Methods

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

1

2

3

4

1

2

Conditional Entropy
• Discretize two dimensions into intervals
• Nested Means

mean

mean

mean

Source: (Guo, 2003)

Conditional Entropy

Source: (Guo, 2003)

Ordering Dimensions
• Related dimensions should be close together

Sort Method: Minimum Spanning Tree

Sort By: Conditional Entropy

A

5

B

9

15

16

21

C

D

4

Ordering: B A D C

unsorted

Demonstration
• 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.