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Advanced self-organizing polynomial neural network

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Abstract

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.

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References

  1. Kim DW (2002) Evolutionary design of self-organizing polynomial neural networks, Master’s thesis, Department Control Instruments Wonkwang University

  2. Oh SK, Pedrycz W (2002) The design of self-organizing polynomial neural networks. Inf Sci 141:237–258

    Article  MATH  Google Scholar 

  3. Oh SK, Kim DW, Park BJ (2000) A study on the optimal design of polynomial neural networks structure. Trans KIEE 49D, No. 3

  4. Jang JS (1993) ANFIS: Adaptive-networks-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  MathSciNet  Google Scholar 

  5. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15:116–132

    Google Scholar 

  6. Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1(1):7–31

    Article  Google Scholar 

  7. Freeman J, Skapura D (1991) Neural networks. Addison-Wesley, New York

    MATH  Google Scholar 

  8. Kodogiannis V, Lolis A (2002) Forecasting financial time series using neural network and fuzzy system-based techniques. Neural Comput Appl 11:90–102

    Article  Google Scholar 

  9. Takagi H, Hayashi I (1991) NN-driven fuzzy reasoning. Int J Approx Reasoning 5(3):191–212

    Article  MATH  Google Scholar 

  10. Funahashi KI (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192

    Article  Google Scholar 

  11. Ivakhnenko AG, Krotov GI, Ivakhnenko NA (1970) Identification of the mathematical model of a complex system by the self-organization method. In: Halfon E (ed) Theoretical systems ecology: advances and case studies, chap 13. Academic, New York

  12. Farlow SJ (1984) Self-organizing methods in modeling, GMDH type-algorithms. Marcel Dekker, New York

    MATH  Google Scholar 

  13. Freeman J, Skapura D (1991) Neural networks. Addison-Wesley, New York

    MATH  Google Scholar 

  14. Fakhr-Eddine K, Cabassud M, Le Lann MV, Couderc JP (2000) Neural network structures for optimal control of LPCVD reactors. Neural Comput Appl 9:172–180

    Article  MATH  Google Scholar 

  15. Kim ET, Park MK, Ji SH, Park M (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 5(3):328–337

    Article  Google Scholar 

  16. Kim E, Lee H, Park M, Park M (1998) A simply identified Sugeno-type fuzzy model via double clustering. Inf Sci 110:25–39

    Article  Google Scholar 

  17. Gomez-Skarmeta AF, Delgado M, Vila MA (1999) About the use of fuzzy clustering techniques for fuzzy model identification. Fuzzy Sets Syst 106:179–188

    Article  Google Scholar 

  18. Hwang HS, Woo KB (1995) Linguistic fuzzy model identification, IEE Proceedings-Control Theory Appl:142(6)

  19. Lin Y, Cunningham III GA (1995) A new approach to fuzzy-neural system modeling. IEEE Trans Fuzzy Syst 3(2):190–198

    Article  Google Scholar 

  20. Kim DW, Oh SK, Kim HK (2001) A study on the self-organizing fuzzy polynomial neural networks. J KIEE 11(2):79–89

    MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors thank the financial support of the Korea Science & Engineering Foundation. This work was supported by grant No. R01-2005-000-11044-0 from the Basic Research Program of the Korea Science & Engineering Foundation. The authors are also very grateful to the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Department of Electrical Engineering, Korea University, 1, 5-ka, Anam-dong, Seongbuk-ku, Seoul, 136-701, South Korea

    Dongwon Kim & Gwi-Tae Park

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  1. Dongwon Kim
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  2. Gwi-Tae Park
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Correspondence to Dongwon Kim or Gwi-Tae Park.

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Kim, D., Park, GT. Advanced self-organizing polynomial neural network. Neural Comput & Applic 16, 443–452 (2007). https://doi.org/10.1007/s00521-006-0070-x

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  • DOI: https://doi.org/10.1007/s00521-006-0070-x

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