Genetically Optimized Self-organizing Neural Networks Based on Polynomial and Fuzzy Polynomial Neurons: Analysis and Design

Abstract

In this study, we introduce and investigate a class of neural architectures of self-organizing neural networks (SONN) that is based on a genetically optimized multilayer perceptron with polynomial neurons (PNs) or fuzzy polynomial neurons (FPNs), develop a comprehensive design methodology involving mechanisms of genetic optimization and carry out a series of numeric experiments. The conventional SONN is based on a self-organizing and an evolutionary algorithm rooted in a natural law of survival of the fittest as the main characteristics of the extended Group Method of Data Handling (GMDH) method, and utilized the polynomial order (viz. linear, quadratic, and modified quadratic) as well as the number of node inputs fixed (selected in advance by designer) at the corresponding nodes (PNs or FPNs) located in each layer through a growth process of the network. Moreover it does not guarantee that the SONN generated through learning results in the optimal network architecture. We distinguish between two kinds of SONN architectures, that is, (a) Polynomial Neuron (PN) based and (b) Fuzzy Polynomial Neuron (FPN) based self-organizing neural networks. This taxonomy is based on the character of each neuron structure in the network. The augmented genetically optimized SONN (gSONN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one encountered in the conventional SONN. The GA-based design procedure being applied at each layer of SONN leads to the selection of preferred nodes (PNs or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial, and a collection of the specific subset of input variables) available within the network. In the sequel, two general optimization mechanisms of the gSONN are explored: the structural optimization is realized via GAs whereas for the ensuing detailed parametric optimization we proceed with a standard least square method-based learning. Each node of the PN based gSONN exhibits a high level of flexibility and realizes a collection of preferred nodes as well as a preferred polynomial type of mapping (linear, quadratic, and modified quadratic) between input and output variables. FPN based gSONN dwells on the ideas of fuzzy rule-based computing and neural networks. The performance of the gSONN is quantified through experimentation that exploits standard data already used in fuzzy or neurofuzzy modeling. These results reveal superiority of the proposed networks over the existing fuzzy and neural models.