“exploring high-d spaces with multiform matrices and small multiples”
DESCRIPTION
“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 PresentationTRANSCRIPT
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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/
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The Plan
Motivation Contribution Analysis Methods GeoVISTA studio Conclusions
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Discover Multivariate relationships
Examine data from multiple perspectives
Motivation
DATA INFORMATION
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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
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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
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Analysis Methods
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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
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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)
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Space-filling visualization
Analysis Methods
Sunburst methodsMosaic plot
Pixel-oriented methods
Source: (Keim, 1996)
Source: (Schedl, 2006)Source: (Young, 1999)
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Multiform Bivariate Small Multiple
Small Multiples A set of juxtaposed data representations that together support understanding of multivariate information
Analysis Methods
Source: (MacEachren, 2003)
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Analysis Methods
Multiform Bivariate Matrix
Source: (MacEachren, 2003)
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GeoVista Studio
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Demonstration
Basic Demo Application construction Scatterplot, Geomap Dynamic linking, eccentric labeling etc.
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Dealing with High Dimensionality
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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.
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High Dimensionality
“Goodness of Clustering” high coverage high density high dependence
E.g. Correlation Chi-squared Conditional Entropy
HIGH
HIGH
LOW
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Conditional Entropy
Discretize two dimensions into intervals Nested Means
mean
mean mean
1 2
1 2 3 4
Source: (Guo, 2003)
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Conditional Entropy
Source: (Guo, 2003)
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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
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Demonstration
Advanced Demo Interactive Feature Selection PCP, SOM, Matrix Conditioning
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Conclusions
Strengths Dynamic Linking of different representations Visualizing clusters of dimensions Rich and extensible toolbox
Weaknesses Usability Arrangement of Windows
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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 .