Analysis of the data concentration function of a four-layer neural network in terms of the autoassociation and PPN models

This paper presents a systematic discussion of the relationship between classical multivariate analysis and various data compression methods arising from the nonlinear mapping capability of multilayer neural networks. The important points of a geometrical interpretation for the case of four or more layers are set down using the well known autoassociation model and the pulse-input/pattern-output network (PPN) model proposed by the authors. Next, the previously unused four-layer autoassociative model is investigated and its effectiveness is demonstrated. Then, the four-layer autoassociative mapping model and the four-layer PPN are compared using a method based on multivariate analysis. That is, it is shown that each method can be related in an approximate fashion to piecewise-linear data compression models as well as to factor analysis models. Finally, to back up these studies, several example experiments are described; a five-layer autoassociative mapping model is then examined, and the data compression capabilities of all three models are compared.