Clustering and Neural Network Approaches

Abstract

This paper describes how clustering problems can be resolved by neural network (NN) approaches such as Hopfield nets, multi-layer perceptrons, and Kohonen’s ’self-organizing maps’ (SOMs). We emphasize the close relationship between the NN approach and classical clustering methods. In particular, we show how SOMs are derived by stochastic approximation from a new continuous version (K-criterion) of a finite-sample clustering criterion proposed by Anouar et al. (1997). In this framework we determine the asymptotic behaviour of Kohonen’s method, design a new finite-sample version of the SOM approach of the k-means type, and propose various generalizations along the lines of classical ’regression clustering’, ’principal component clustering’, and ’maximum-likelihood clustering’.KeywordsStochastic ApproximationCluster CriterionClass CenterHopfield NetworkStochastic Approximation AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.