Dynamic behavior of DCT and DDT formulations for the Sanger neural network

In this paper, the behavior of the Sanger hebbian artificial neural networks is analyzed. Hebbian networks are employed to implement principal component analysis (PCA), and several improvements over the original model due to Oja have been developed in the last two decades. Among them, Sanger model is designed to directly provide the eigenvectors of the correlation matrix. The behavior of these models has been traditionally considered on a deterministic continuous-time (DCT) formulation whose validity is justified under some hypotheses on the specific asymptotic behavior of the learning gain. In practical applications, these assumptions cannot be guaranteed. This paper addresses a comparative study with a deterministic discrete-time (DDT) formulation that characterizes the average evolution of the net, preserving the discrete-time form of the original network and gathering a more realistic behavior of the learning gain. The results thoroughly characterize the relationship between the learning gain and the eigenvalue structure of the correlation matrix.