Abstract
We introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose topology is developed through learning; it is a self-organizing network. PNN has two kinds of networks, polynomial neuron-based and fuzzy polynomial neuron (FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based self-organizing polynomial neural networks(SOPNN) dwells on the group method of data handling. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neuro-fuzzy systems. A detailed comparative analysis is also included.