Constrained Learning in Neural Networks: Application to Stable Factorization of 2-D Polynomials

Authors:
Stavros Perantonis;Nikolaos Ampazis;Stavros Varoufakis;George Antoniou
Affiliations:
Institute of Informatics and Telecommunications, National Center for Scientific Research ’Demokritos‘, 153 10 Aghia Paraskevi, Athens, Greece;Institute of Informatics and Telecommunications, National Center for Scientific Research ’Demokritos‘, 153 10 Aghia Paraskevi, Athens, Greece;Institute of Informatics and Telecommunications, National Center for Scientific Research ’Demokritos‘, 153 10 Aghia Paraskevi, Athens, Greece;Department of Mathematics and Computer Science, Montclair State University, Montclair, New Jersey 07043, USA
Venue:
Neural Processing Letters
Year:
1998

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Abstract

Adaptive artificial neural network techniques are introduced and appliedto the factorization of 2-D second order polynomials. The proposed neuralnetwork is trained using a constrained learning algorithm that achievesminimization of the usual mean square error criterion along withsimultaneous satisfaction of multiple equality and inequality constraintsbetween the polynomial coefficients. Using this method, we are able toobtain good approximate solutions for non-factorable polynomials. Byincorporating stability constraints into the formalism, our method can besuccessfully used for the realization of stable 2-D second order IIR filtersin cascade form.