Visualizing Clusters in Artificial Neural Networks Using Morse Theory

Document Type

Article

Publication Date

Spring 6-5-2013

Publication Source

Advances in Artificial Neural Systems

Volume Number

2013

Issue Number

486363

First Page

1

Last Page

8

Publisher

Hindawi Publishing Corporation

Article Number

486363

Comments

http://www.hindawi.com/journals/aans/2013/486363/

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.

Keywords

Artificial Neural Network, Morse Theory, Diabetes, Clustering, Topological Data Analysis

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