Factorization of 2-D polynomials using neural networks and constrained learning techniques

A method is presented for factorizing two-dimensional polynomials, with the aim of designing 2-D IIR filters in cascade form. A specialized neural network structure is employed which is a variation of a two-layer sigma-pi neural network paradigm. By training the network to emulate a given polynomial, the lower-order factor polynomials are generated whose coefficients are represented by the network's weights. While the simple learning rule based on gradient descent sometimes fails to give satisfactory results, a new modified learning rule is proposed which is based on constrained optimization techniques. The proposed method achieves minimization of the usual mean-square error criterion along with a simultaneous satisfaction of constraints between the coefficients of the given polynomial and the coefficients of the desired factor polynomials. Using this approach, suitably augmented by weight elimination techniques, we are able to obtain exact solutions for factorable polynomials and excellent approximate solutions for non-factorable polynomials. Simulations are presented to illustrate the good performance and efficiency of the proposed method.