Local analysis of a new Rubner-type neural network via a DDT formulation

Abstract

In this paper, the behavior of the Rubner Hebbian artificial neural network is analyzed. Hebbian neural networks are employed in communications and signal processing applications, among others, due to their capability to implement principal component analysis (PCA). Different improvements over the original model due to Oja have been developed in the last two decades. Among them, Sanger and Rubner models were designed to directly provide the eigenvectors of the correlation matrix. The behavior of these models has been traditionally considered on a continuous-time formulation whose validity is justified via some analytical procedures that presume, among other hypotheses, an specific asymptotic behavior of the learning gain. In practical applications, these assumptions cannot be guaranteed. This paper addresses the study of a deterministic discrete-time (DDT) formulation of the Rubner net, that characterizes the average evolution of the net, preserving the discrete-time form of the original network and gathering the influence of the learning gain. This way, the dynamical behavior of Rubner model is analyzed in this more realistic context. The results thoroughly characterize the relationship between the learning gain and the eigenvalue structure of the correlation matrix.