Visualizing Clusters in Artificial Neural Networks Using Morse Theory

Abstract

This paper develops a process whereby a high-dimensional clustering problem is solved using a neural network and a lowdimensional cluster diagram of the results is produced using the Mapper method from topological data analysis. The lowdimensional 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 froma 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.