AbstractThis 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