CROSS-CORRELATION NEURAL-NETWORK MODELS FOR THE SMALLEST SINGULAR COMPONENT OF GENERAL MATRIX

In this paper, we provide the theoretical foundation for a novel neura l model to solve the smallest singular component of general matrix, on the basis of an extension of the Hebbian rule and a modification of c ross-coupled Hebbian rule. This model can efficiently extract the sing ular-value component of the cross-correlation matrix of two stochastic signals. By Lasalle's invariance principle and Lyapunov's indirect me thod, we study the global asymptotic convergence of the networks to th e first singular vectors of the cross-correlation matrix or non-square s matrix. A comparative study on the related neural networks shows tha t this neural network is efficient for computing the smallest singular component of general matrix. The novel model may have useful applicat ions in solving the total least-squares problems in adaptive signal pr ocessing and image compressing. (C) 1998 Elsevier Science B.V. All rig hts reserved.