The Whitney Reduction Network: A method for computing autoassociative graphs

This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an ni-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motiv ated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of th e original data may be achieved for some d less than or equal to 2m + 1. To implement this network, we propose the idea of a good-projection, which en hances the generalization capabilities of the network, and an adaptive seca nt basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.