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# “Exploring High-D Spaces with Multiform Matrices and Small Multiples” - PowerPoint PPT Presentation

“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 Multiples”

• Motivation

• Contribution

• Analysis Methods

• GeoVISTA studio

• Conclusions

Motivation Multiples”

• Discover Multivariate relationships

• Examine data from multiple perspectives

DATA  INFORMATION

Contribution Multiples”

• Visual analysis of multivariate data

• Combinations of scatterplots, bivariate maps and space-filling displays

• Dynamic query/filtering called Conditioning

Contribution Multiples”

• 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 Multiples”

Sorting Multiples”

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 Multiples”

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 Multiples”

Analysis Methods

Mosaic plot

Sunburst methods

Source: (Schedl, 2006)

Source: (Young, 1999)

Pixel-oriented methods

Source: (Keim, 1996)

Multiform Bivariate Small Multiple Multiples”

Analysis Methods

• Small Multiples

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

Source: (MacEachren, 2003)

Multiform Bivariate Matrix Multiples”

Analysis Methods

Source: (MacEachren, 2003)

### GeoVista Studio Multiples”

Demonstration Multiples”

• Basic Demo

• Application construction

• Scatterplot, Geomap

• Dynamic linking, eccentric labeling etc.

### Dealing with High Dimensionality Multiples”

High Dimensionality Multiples”

• 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 Multiples”

• “Goodness of Clustering”

• high coverage

• high density

• high dependence

• E.g.

• Correlation

• Chi-squared

• Conditional Entropy

HIGH

HIGH

LOW

1 Multiples”

2

3

4

1

2

Conditional Entropy

• Discretize two dimensions into intervals

• Nested Means

mean

mean

mean

Source: (Guo, 2003)

Conditional Entropy Multiples”

Source: (Guo, 2003)

Ordering Dimensions Multiples”

• 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 Multiples”

• Interactive Feature Selection

• PCP, SOM, Matrix

• Conditioning

Conclusions Multiples”

• Strengths

• Dynamic Linking of different representations

• Visualizing clusters of dimensions

• Rich and extensible toolbox

• Weaknesses

• Usability

• Arrangement of Windows

References Multiples”

• 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.