NONLINEAR DATA STRUCTURE EXTRACTION USING SIMPLE HEBBIAN NETWORKS

We present a class a neural networks algorithms based on simple hebbia n learning which allow the finding of higher order structure in data. The neural networks use negative feedback of activation to self-organi se; such networks have previously been shown to be capable of performi ng principal component analysis (PCA). In this paper, this is extended to exploratory projection pursuit (EPP), which is a statistical metho d for investigating structure in high-dimensional data sets. As oppose d to previous proposals for networks which learn using hebbian learnin g, no explicit weight normalisation, decay or weight clipping is requi red. The results are extended to multiple units and related to both th e statistical literature on EPP and the neural network literature on n on-linear PCA.