1. Jewels, Himalayas and Fireworks, Extending Methods for
Visualizing N Dimensional Clustering
W. Jockheck
Dept. of Computer Science
North Dakota State University
Fargo, North Dakota 58105
Dr. William Perrizo
CATA March 2010

2. Overview
Visualization of high dimensional data is awkward and in some cases leads to incorrect conclusions.
The human mind is the most sophisticated and effective pattern recognition device available for two-dimensional (or three-dimensional) patterns.
This paper considers “pattern preserving” (cluster preserving) transformations of high dimensional data into two dimensional space.
The techniques enable quick visual scans which can yield significant amounts of pattern related information.
Then other methods can be used for further drill down.
CATA March 2010

3. Visualizing N Dimensional Clustering
Chernoff's faces
Parallel Coordinates
Jewel Diagram
CATA March 2010

4. Table Columns as Dimensions
A table of n numeric columns can be considered as a set of points in n dimensional space (e.g., the 1st 4 IRIS columns).
CATA March 2010

5. Projecting Hypercube into 2D
When projecting an arbitrary vector is used for each dimensional axis.
Five dimensional hypercube using the axis indicated.
CATA March 2010

6. Jewel Diagram and Projections
The single combined points in the jewel diagram represent an n-dimensional projection using the sides of the polygon as the axis of the dimensions.
CATA March 2010

7. Jewel Diagram Revisited
Other methods of projecting points
Variations on parallel coordinates
Himalayan variation A1 A5
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8. Jewel Diagram Revisited
Himalayan and odd sided polygon versions
CATA March 2010

9. Adjustments and Fixes
Variations on the arrangement and directionality of the axis were explored.
In some variations pairs of attributes off set each other.
Generally, parallel or similar axis were found to minimize visibility of differences.
This lead to placing all axis in a single quadrant (so that they don’t cancel out each other’s effects).
CATA March 2010

10. Single Quadrant Variations
Uniform Axis Spacing
Himalayan Axis Spacing
CATA March 2010

11. Fireworks
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12. Injection of Noise
To test the sensitivity to noise, additional attributes were added to the iris data that were random.
In addition various method of favoring and arranging attributes were tested.
CATA March 2010

13. Variations with Weighting and Noise
Iris data
With Noise
All
Weighted
CATA March 2010

14. X
Why not 3D instead of 2D
VRML version was a “3D” implementation with samples slightly offset in the Z axis.
2D rant
Humans only see in 2D. The retina, while curved only captures a 2D projection.
Computer displays are 2D.
Printed outputs are 2D.
VRML only allows the modification of the projection into 2D.
CATA March 2010

15. Problems As n increases Sequence attributes (sides /axes)
Jewel diagram polygon approaches a circle.
Fireworks axes become indistinguishable.
Projected points tend to overlap and obscure.
Possibility of coincident points increases.
Sequence attributes (sides /axes)
Alter projected point distribution.
Convey different information.
CATA March 2010

16. Problem Mitigation The reality of points and lines.
Point has no dimensions, only location.
Lines have no width.
The reality of displays.
Points have to have dimension to be visible.
Lines have to have width to be visible.
Scaling as a solution.
CATA March 2010

17. Contribution of the Visualization
Single projected point represents sample showing its relationship in the data set.
Provides display of each attribute distribution.
Provides visual input, full picture for the user.
CATA March 2010

18. Summary Jewel / Fireworks Visualization of Dimensions beyond 3
Provides a single point projection for each sample (tuple).
Computationally simple
Very modifiable and adaptable
Colors, sequences, weighting, scaling
CATA March 2010

19. Jewels, Himalayas and Fireworks, Extending Methods for
Visualizing N Dimensional Clustering
W. Jockheck
Dept. of Computer Science
North Dakota State University
Fargo, North Dakota 58105
Dr. William Perrizo
CATA March 2010