Polynomial-based radial basis function neural networks (P-RBF NNs) realized with the aid of particle swarm optimization

Authors:
Sung-Kwun Oh;Wook-Dong Kim;Witold Pedrycz;Byoung-Jun Park
Affiliations:
Department of Electrical Engineering, University of Suwon, Hwaseong-si, Gyeonggi-do, South Korea;Department of Electrical Engineering, University of Suwon, Hwaseong-si, Gyeonggi-do, South Korea;Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Canada T6R 2G7 and Systems Science Institute, Polish Academy of Sciences Warsaw, Poland;Spatial Information Research Team, Telematics & USN Research Department, IT Convergence Technology Research Laboratory, Electronics and Telecommunications Research Institute (ETRI), 161 Gajeong-do ...
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

In this study, we design polynomial-based radial basis function neural networks (P-RBF NNs) based on a fuzzy inference mechanism. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient of the underlying clustering method) are optimized by means of the particle swarm optimization. The proposed P-RBF NNs dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy C-means (FCM). The network is of functional nature as the weights between the hidden layer and the output are some polynomials. The use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems. From the perspective of linguistic interpretation, the proposed network can be expressed as a collection of ''if-then'' fuzzy rules. The architecture of the networks discussed here embraces three functional modules reflecting the three phases of input-output mapping realized in rule-based architectures, namely condition formation, conclusion creation, and aggregation. The proposed classifier is applied to some synthetic and machine learning datasets, and its results are compared with those reported in the previous studies.