ON SELF-ORGANIZING ALGORITHMS AND NETWORKS FOR CLASS-SEPARABILITY FEATURES

We describe self-organizing learning algorithms and associated neural networks to extract features that are effective for preserving class s eparability. As a first step, an adaptive algorithm for the computatio n of Q(-1/2) (where Q is the correlation or covariance matrix of a ran dom vector sequence) is described, Convergence of this algorithm with probability one is proven by using stochastic approximation theory, an d a single-layer linear network architecture for this algorithm is des cribed, which we call the Q(-1/2) network, Using this network, we desc ribe feature extraction architectures for: 1) unimodal and multicluste r Gaussian data in the multiclass case; 2) multivariate linear discrim inant analysis (LDA) in the multiclass case; and 3) Bhattacharyya dist ance measure for the two-class case. The LDA and Bhattacharyya distanc e features are extracted by concatenating the Q(-1/2) network with a p rincipal component analysis (PCA) network, and the two-layer network i s proven to converge with probability one. Every network discussed in the study considers a how or sequence of inputs for training, thereby eliminating the need for a pooled data for training, and making the ne tworks useful for online applications, Furthermore, the training of al l layers of the networks can proceed simultaneously, Numerical studies on the performance of the networks for multiclass random data are pre sented.