Design of Space Search-Optimized Polynomial Neural Networks with the Aid of Ranking Selection and L2-norm Regularization

The conventional polynomial neural network (PNN) is a classical flexible neural structure and self-organizing network, however it is not free from the limitation of overfitting problem. In this study, we propose a space search-optimized polynomial neural network (ssPNN) structure to alleviate this problem. Ranking selection is realized by means of ranking selection-based performance index (RS_PI) which is combined with conventional performance index (PI) and coefficients based performance index (CPI) (viz. the sum of squared coefficient). Unlike the conventional PNN, L2-norm regularization method for estimating the polynomial coefficients is also used when designing the ssPNN. Furthermore, space search optimization (SSO) is exploited here to optimize the parameters of ssPNN (viz. the number of input variables, which variables will be selected as input variables, and the type of polynomial). Experimental results show that the proposed ranking selection-based polynomial neural network gives rise to better performance in comparison with the neuron fuzzy models reported in the literatures.