Dz. Feng et al., CROSS-CORRELATION NEURAL-NETWORK MODELS FOR THE SMALLEST SINGULAR COMPONENT OF GENERAL MATRIX, Signal processing, 64(3), 1998, pp. 333-346
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.