A note on the low-dimensional display of multivariate data using neural networks.

Abstract

A novel neural network technique has been proposed (Livingstone et al. J. Mol. Graphics 1991, 9, 115-118) which is useful for a low-dimensional display of multivariate data sets. The method makes use of the activity values of the hidden neurons in a trained three-layer feed-forward network to produce the low-dimensional display. It was claimed that in contrast to conventional techniques, such as principal components analysis or nonlinear mapping, this technique could be used also to reconstruct, from a given point in the low-dimensional display, the corresponding multivariate input vector via the completely known weight matrices of a suitably trained network. We show here that this claim is unjustified in this general form. When previously unknown, grossly different input vectors are presented to the trained network, they can occupy, for example, exactly the same point in the low-dimensional display which is occupied also by a given training vector, if certain linear relationships between the vector components are fulfilled. Thus, an infinite set of different linearly dependent input vectors is projected onto one single point in the low-dimensional display. Reconstruction of a multivariate vector, starting from this point in the low-dimensional display, is able to lead back to only one multivariate vector (in the example given, to the original training vector).