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A new approach to radial basis function-based polynomial neural networks: analysis and design

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Abstract

In this study, we introduce a new topology of radial basis function-based polynomial neural networks (RPNNs) that is based on a genetically optimized multi-layer perceptron with radial polynomial neurons (RPNs). This paper offers a comprehensive design methodology involving various mechanisms of optimization, especially fuzzy C-means (FCM) clustering and particle swarm optimization (PSO). In contrast to the typical architectures encountered in polynomial neural networks (PNNs), our main objective is to develop a topology and establish a comprehensive design strategy of RPNNs: (a) The architecture of the proposed network consists of radial polynomial neurons (RPN). These neurons are fully reflective of the structure encountered in numeric data, which are granulated with the aid of FCM clustering. RPN dwells on the concepts of a collection of radial basis function and the function-based nonlinear polynomial processing. (b) The PSO-based design procedure being applied to each layer of the RPNN leads to the selection of preferred nodes of the network whose local parameters (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, the number of clusters of FCM clustering, and a fuzzification coefficient of the FCM method) are properly adjusted. The performance of the RPNN is quantified through a series of experiments where we use several modeling benchmarks, namely a synthetic three-dimensional data and learning machine data (computer hardware data, abalone data, MPG data, and Boston housing data) already used in neuro-fuzzy modeling. A comparative analysis shows that the proposed RPNN exhibits higher accuracy in comparison with some previous models available in the literature.

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Acknowledgments

This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (NRF-2012-003568) and supported by the GRRC program of Gyeonggi province (GRRC SUWON 2012-B2, Center for U-city Security & Surveillance Technology).

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Suwon, Hwaseong-si, Gyeonggi-do, South Korea

    Sung-Kwun Oh & Wook-Dong Kim

  2. Honam Leading Industry Office, Gwangju, South Korea

    Ho-Sung Park

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6R 2G7, Canada

    Witold Pedrycz

  4. System Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Witold Pedrycz

Authors
  1. Sung-Kwun Oh
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  2. Ho-Sung Park
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  3. Wook-Dong Kim
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  4. Witold Pedrycz
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Correspondence to Sung-Kwun Oh.

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Oh, SK., Park, HS., Kim, WD. et al. A new approach to radial basis function-based polynomial neural networks: analysis and design. Knowl Inf Syst 36, 121–151 (2013). https://doi.org/10.1007/s10115-012-0551-4

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  • DOI: https://doi.org/10.1007/s10115-012-0551-4

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