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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 - PowerPoint PPT Presentation
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“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 .