Multi-layer self-organizing polynomial neural networks and their development with the use of genetic algorithms

In this paper, we introduce a new architecture of genetic algorithms (GA)-based self-organizing polynomial neural networks (SOPNN) and discuss a comprehensive design methodology. Let us recall that the design of the “conventional” PNNs uses an extended group method of data handling (GMDH) and exploits polynomials (such as linear, quadratic, and modified quadratic functions) as well as considers a fixed number of input nodes (as being selected in advance by a network designer) at polynomial neurons (or nodes) located in each layer. The proposed GA-based SOPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional PNNs. The design procedure applied in the construction of each layer of a PNN deals with its structural optimization involving the selection of preferred nodes (or PNs) 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) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the network. To evaluate the performance of the GA-based SOPNN, the model is experimented with using chaotic time series data. A comparative analysis reveals that the proposed GA-based SOPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.