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Advances in Artificial Neural Systems
Volume 2013 (2013), Article ID 486363, 8 pages
http://dx.doi.org/10.1155/2013/486363
Research Article

Visualizing Clusters in Artificial Neural Networks Using Morse Theory

Department of Mathematics, Hope College, P.O. Box 9000, Holland, MI 49422-9000, USA

Received 27 March 2013; Revised 31 May 2013; Accepted 5 June 2013

Academic Editor: Songcan Chen

Copyright © 2013 Paul T. Pearson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper develops a process whereby a high-dimensional clustering problem is solved using a neural network and a low-dimensional cluster diagram of the results is produced using the Mapper method from topological data analysis. The low-dimensional cluster diagram makes the neural network's solution to the high-dimensional clustering problem easy to visualize, interpret, and understand. As a case study, a clustering problem from a diabetes study is solved using a neural network. The clusters in this neural network are visualized using the Mapper method during several stages of the iterative process used to construct the neural network. The neural network and Mapper clustering diagram results for the diabetes study are validated by comparison to principal component analysis.