Hierarchical polynomial-based fuzzy neural networks driven with the aid of hybrid network architecture and ranking-based neuron selection strategies

Abstract In this study, we propose hierarchical polynomial-based fuzzy neural networks (HPFNN). The aim of this study is to develop the design methodologies of hierarchical model to improve the prediction accuracy of the model without sacrificing computational efficiency through combining hybrid network architecture composed of different neurons and ranking-based neuron selection strategies. The essential bullets of the proposed model can be enumerated as follows: (a) A hybrid network architecture is designed by combining the traits of fuzzy rule-based neurons with random vector functional link (FRN-RVFL) and polynomial neurons. FRN-RVFL is employed to erect the first layer of network. The entire network topology and the neurons of the remaining layers are constructed with polynomial neural network. (b) Two kinds of ranking-based neuron selection (RNS) strategies such as Linear-RNS (LRNS) and Exponential-RNS (EPNS) are presented. Compared with traditional neuron selection strategy, RNS can enrich the diversity of candidate neurons while maintaining the approximation ability of neurons, which provides opportunities for selecting neurons with predictive potential. (c) Regularization-based least square approach is applied to alleviate the possible overfitting in coefficient estimation as well as enhance generalization abilities of the model. The performance of HPFNN is verified by using a series of synthetic data and machine learning datasets. Based on the experimental results, HPFNN exhibits sound prediction accuracy and reasonable computational cost in contrast with the same type of hierarchical models. Furthermore, HPFNN achieves better generalization performance on at least 12 of 20 datasets when compared with the performance of state-of-the-art models.