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

S. J. Perantonis, N. Ampazis, S. J. Varoufakis, George Antoniou

Research output: Contribution to conferencePaperResearchpeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages1276-1280
Number of pages5
StatePublished - 1 Dec 1997
EventProceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3) - Guimaraes, Portugal
Duration: 7 Jul 199711 Jul 1997

Other

OtherProceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3)
CityGuimaraes, Portugal
Period7/07/9711/07/97

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Factorization
Polynomials
Neural networks
IIR filters
Constrained optimization
Mean square error

Cite this

Perantonis, S. J., Ampazis, N., Varoufakis, S. J., & Antoniou, G. (1997). Factorization of 2-D polynomials using neural networks and constrained learning techniques. 1276-1280. Paper presented at Proceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3), Guimaraes, Portugal, .
Perantonis, S. J. ; Ampazis, N. ; Varoufakis, S. J. ; Antoniou, George. / Factorization of 2-D polynomials using neural networks and constrained learning techniques. Paper presented at Proceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3), Guimaraes, Portugal, .5 p.
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Perantonis, SJ, Ampazis, N, Varoufakis, SJ & Antoniou, G 1997, 'Factorization of 2-D polynomials using neural networks and constrained learning techniques' Paper presented at Proceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3), Guimaraes, Portugal, 7/07/97 - 11/07/97, pp. 1276-1280.

Factorization of 2-D polynomials using neural networks and constrained learning techniques. / Perantonis, S. J.; Ampazis, N.; Varoufakis, S. J.; Antoniou, George.

1997. 1276-1280 Paper presented at Proceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3), Guimaraes, Portugal, .

Research output: Contribution to conferencePaperResearchpeer-review

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N2 - 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.

AB - 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.

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Perantonis SJ, Ampazis N, Varoufakis SJ, Antoniou G. Factorization of 2-D polynomials using neural networks and constrained learning techniques. 1997. Paper presented at Proceedings of the 1997 IEEE International Symposium on Industrial Electronics, ISIE. Part 3 (of 3), Guimaraes, Portugal, .