Representing High-Dimensional Data Sets as Closed Surfaces

Abstract

Scientific data visualization provides scientists and engineers with a deeper insight and greater understanding about physical phenomena through the use of graphical tools. Individuals are able to identify patterns embedded in data sets using visual cues such as color and shape, rather than directly searching through a vast volume of numbers. The visualization algorithm described in this paper utilizes a spherical self-organizing feature map (SOFM) to automatically cluster and develop a well-defined topology of arbitrary data vectors, based on a pre-defined measure of similarity, and generate a three-dimensional color-coded surface model that reflects cluster variations. Implementation of this self-organizing surface geometry for data visualization applications is illustrated by examining the graphical forms created for a small synthetic test data set and a large environmental data-base. The proposed methodology provides the researcher with a new tool to encode information into shape and easily transfer the geometric model to an immersive virtual reality (IVR) environment for interactive information analysis.

Keywords

Scientific data visualization interactive information analysis self-organizing feature map spherical representations

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References

Ware

Information Visualization: Perception for Design. Morgan Kaufmann publishers: San Francisco, CA, 1999; 1–33.

Nielson

Hagen

Müller

Scientific Visualization: Overviews, Methodologies, Techniques. IEEE Computer Society Press: NJ, 1997.

Wise

. Change as a Concept in Information System Theory. PhD thesis submitted to the Faculty of Interdisciplinary Department of Information Science, the University of Pittsburgh, 1977.

Cleveland

McGill

Theory, experimentation and applications to the development of graphical methods. Journal of the American Statistical Association 1984; 79 (387): 531–554.

Cleveland

McGill

The visual decoding of quantitative information on graphical displays of data. Journal of the Royal Statistical Society (Series A) 1987; 150 (3): 192–229.

Ebert

Rohrer

Shaw

Panda

Kukla

Roberts

. Procedural shape generation for multi-dimensional data visualization. Computers and Graphics 2000; 24: 375–384.

Chernoff

The use of faces to represent points in k-dimensional space graphically. Journal of American Statistical Association 1973; 68 (342): 361–368.

Fayyad

Grinstein

Wierse

Information Visualization in Data Mining and Knowledge Discovery. Morgan Kaufmann Publishers: CA, 2002.

Rohrer

Sibert

Ebert

. A shape-based visual interface for text retrieval. IEEE Computer Graphics and Applications 1999; 19 (5): 40–46.

10.

Kaski

Data Exploration using Self-organizing Maps. PhD thesis submitted to the Neural Network Research Center, Helsinki University of Technology, 1997.

11.

Knopf

Sangole

Visualizing data association using self-organizing feature maps. In: Dagli

(Ed.). Intelligent Engineering Systems Through Artificial Neural Networks. ASME Press: New York, NY, 2000; 471–476.

12.

Ritter

Self-organizing maps on non-Euclidean spaces. In: Oja

Kaski

(Ed.). Kohonen Maps. Elsevier Science BV: Amsterdam, The Netherlands, 1999; 97–109.

13.

Vesanto

SOM-based data visualization methods. Journal of Intelligent Data Analysis 1999; 3 (2): 111–126.

14.

Ultsch

Siemon

. Kohonen's self-organizing feature maps for exploratory data analysis. Proceedings of the International Neural Network Conference (Dordrecht, The Netherlands), 1990; 305–308.

15.

DesJardins

Rheingans

Visualization of high-dimensional model characteristics. Workshop on New Paradigms in Information Visualization and Manipulation (NPIVM1999), ACM Press: New York, NY, 1999; 6–8.

16.

Busch

Gross

Interactive neural network texture analysis and visualization for surface reconstruction in medical mapping. Proceedings of Eurographics' 93 1993; 12 (3): C49–C60.

17.

Gross

Seibert

Visualization of multi-dimensional image data sets using a neural network. The Visual Computer, International Journal of Computer Graphics 1993; 10 (1): 145–159.

18.

Gross

Visual Computing: The Integration of Computer Graphics, Visual Perception and Imaging. Springer-Verlag: Berlin, 1994.

19.

Kohonen

Self-Organizing Maps. Springer: New York, 1997.

20.

Krishnamurthy

Ahalt

Melton

Chen

Neural networks for vector quantization of speech and images. IEEE Journal on Selected Areas in Communication 1990; 8 (8): 1449–1457.

21.

Hebert

Ikeuchi

Delingette

A spherical representation for recognition of free-form surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence 1995; 17 (7): 681–690.

22.

Duda

Hart

. Pattern Classification and Scene Analysis. John Wiley & Sons: CA, 1973.

23.

Ames

Nadeau

Moreland

. The VRML 2.0 Sourcebook. John Wiley & Sons: NY, 1997.

24.

Hall

Meeson

Los

Steyaert

de Colstoun

Landis

(eds). ISLSCP Initiative II, NASA DVD/CD-ROM. NASA, 2002.