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Recursive clustering based on a Gustafson–Kessel algorithm

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Abstract

In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey–Glass time series prediction are also given.

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References

  • Angelov P (2004) An approach for fuzzy rule-base adaptation using on-line clustering. Integration of Methods and Hybrid Systems 35(3):275–289

    MATH  MathSciNet  Google Scholar 

  • Angelov P (2010) Evolving Takagi–Sugeno fuzzy systems from streaming data (eTs+). In: Angelov P, Filev D, Kasabov A (eds) Evolving intelligent systems: methodology and applications, Willey, IEE Press Series on Computational Intellegence, pp 273–300

  • Angelov P, Zhou X (2006) Evolving Fuzzy Systems from Data Streams in Real-Time, 2006 International Symposium on Evolving Fuzzy Systems, 7–9 September, 2006, Ambelside, Lake District, UK, IEEE Press, pp 29–35

  • Angelov PP (2002) Evolving rule-based models: a tool for design of flexible adaptive systems. Springer-Verlag, Heidelberg

    MATH  Google Scholar 

  • Angelov PP, Filev DP (2004) An approach to online identification of Takagi–Sugeno fuzzy models. IEEE Trans Syst Man Cyber part B 34(1):484–497

    Article  Google Scholar 

  • Åström KJ, Wittenmark B (1995) Adaptive control. Addison-Wesley, New York

    MATH  Google Scholar 

  • Azeem MF, Manmandlu M, Ahmad N (1999) Modified mountain clustering in dynamic fuzzy modeling, 2nd Int. Conf. Inform. Technol, Bhubaneswar, pp 63–68

  • Azeem MF, Hanmandlu M, Ahmad N (2003) Structure identification of generalized adaptive neuro-fuzzy inference systems. IEEE Trans on Fuzzy Syst 11(5):666–681

    Article  Google Scholar 

  • Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    MATH  Google Scholar 

  • Chiu SL (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2:267–278

    MathSciNet  Google Scholar 

  • Dovžan D, Škrjanc I (2010) Fuzzy predictive functional control with adaptive fuzzy model. In: IEEE International Joint Conferences on Computational Cybernetics and Technical Informatics (ICCC-CONTI 2010), Timisoara, Romania, pp 143–147, 27–29 May 2010

  • Filev D, Georgieva O (2010) An extended version of the Gustafson–Kessel algorithm for evolving data stream clustering. In: Angelov P, Filev D, Kasabov A (eds) Evolving Intelligent Systems: Methodology and Applications. Willey, IEE Press Series on Computational Intellegence, pp 273–300

  • Goodwin GC, Sin KS (1984) Adaptive filtering prediction and control. Prentice-Hall, Upper Saddle River, New York

    MATH  Google Scholar 

  • Gustafson D, Kessel W (1979) Fuzzy clustering with fuzzy covariance matrix, In: Proceedings of IEEE CDC, San Diego, CA, USA, pp 761–766

  • Hai-Jun Rong, Sundararajan N, Guang-Bin Huang, Saratchandran P (2006) Adaptive fuzzy inference system (SAFIS) for nonlinear system identification and prediction. Fuzzy Sets Syst 157(9):1260–1275

    Article  MATH  Google Scholar 

  • Henson MA, Seborg DE (1994) Nonlinear control of a pH neutralization process. IEEE Trans Control Syst Technol 2(3):169–182

    Article  Google Scholar 

  • Hwang CL, Chang LJ (2007) Neural-based control for nonlinear time-varying delay systems. IEEE Trans Syst Man Cyber part B 37(6):1471–1485

    Article  Google Scholar 

  • Johanson TA, Murray-Smith R (1997) The operating regime approach to nonlinear modeling and control. In: Murray-Smith R, Johanson TA (eds) Multiple model approaches to modeling and control. Taylor & Francis, London, pp 3–72

  • Juang CF, Lin CT (1998) An on-line self-constructing neural fuzzy inference network and its applications. IEEE Trans on Fuzzy Syst 6(1):12–32

    Article  Google Scholar 

  • Kasabov N (1996) Learning fuzzy rules and approximate reasoning in fuzzy neural networks and hybrid systems. Fuzzy Sets Syst 82(2):665–685

    MathSciNet  Google Scholar 

  • Kasabov N (1998a) ECOS: a framework for evolving connectionist systems and the ECO learning paradigm. In: Proceedings of ICONIP 1998, Japan, pp 1222–1235

  • Kasabov N (1998b) Evolving fuzzy neural networks-algorithms, applications and biological motivation. Methodologies for the conceptation. Design and Application of Soft Computing, Singapore, pp 271–274

  • Kasabov N (2001) Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning. IEEE Trans Syst Man Cyber part B 31(6):902–918

    Article  Google Scholar 

  • Kasabov NK, Song Q (2002) Dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Trans on Fuzzy Syst 10(2):144–154

    Article  Google Scholar 

  • Kim E, Minkee Park, Ji S, Migon Park (1997) A new approach to fuzzy modeling. IEEE Trans on Fuzzy Syst 5(3): 328–337

  • Kim K, Baek J, Kim E, Park M (2005) TSK Fuzzy model based on-line identification. In: Proceedings of 11th IFSA World Congress, Beijing, China, pp 1435–1439

  • Kukolj D, Levi E (2004) Identification of complex systems based on neural and Takagi Sugeno fuzzy model. IEEE Trans Syst Man Cyber part B 34(1):272–282

    Article  Google Scholar 

  • Leng G, Prasad G, McGinnty TM (2004) On-line algorithm for creating self-organizing fuzzy neural networks. Neural Networks 17(10):1477–1493

    Article  MATH  Google Scholar 

  • Lin CT (1995) A neural fuzzy control system with structure and parameter learning. Fuzzy Sets Syst 70:183–212

    Article  Google Scholar 

  • Lin F-J, Lin C-H, Shen P-H (2001) Self-constructing fuzzy neural network speed controller for permanent-magnet synchronous motor drive. IEEE Trans Fuzzy Syst 9(5):751–759

    Article  Google Scholar 

  • Mackey MC, Glass L (1977) Oscilations and chaos in physiological control systems. Sci Agric 197:287–289

    Google Scholar 

  • Paiva RP, Dourado A (2001) Structure and parameter learning of neuro-fuzzy systems: a methodology and a comparative study. J Intell Fuzzy Syst 11:147–161

    Google Scholar 

  • Qiao J, Wang H (2008) A self-organizing fuzzy neural network and its applications to function approximation and forecast modeling. Neurocomputing 71(4–6):564–569

    Article  Google Scholar 

  • Shing J, Jang R (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cyber 23(3):665–685

    Article  Google Scholar 

  • Škrjanc I, Matko D (2000) Predictive functional control based on fuzzy model for heat-exchanger pilot plant. IEEE Trans Fuzzy Syst 8(6):705–712

    Article  Google Scholar 

  • Soleimani-B H, Lucas C, Araabi BN (2010) Recursive Gath-Geva clustering as a basis for evolving neuro-fuzzy modeling, Evolving Systems, Springer 1(1):59–71. doi:10.1007/s12530-010-9006-x

  • Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications. IEEE Trans Syst Man Cyber, vol SMC-15, 116–132

  • Tzafestas SG, Zikidis KC (2001) NeuroFAST: On-Line Neuro-Fuzzy ART-Based Structure and Parameter Learning TSK Model. IEEE Trans Syst Man Cyber part B 31(5):797–802

    Article  Google Scholar 

  • Wang D, Xiao-Jun Zeng, Keane JA (2008) An incremental construction learning algorithm for identification of T–S Fuzzy Systems. In: Proceedings of FUZZ 2008 (IEEE International Conference on Fuzzy Systems 2008), Hong Kong, pp 1660–1666

  • Wu S, Er MJ (2000) Dynamic fuzzy neural networksa novel approach to function approximation. IEEE Trans Syst Man Cyber part B 30(2):358–364

    Article  Google Scholar 

  • Wu S, Er MJ, Gao Y (2001) A fast approach for automatic generation of fuzzy rules by generalized dynamicc fuzzy neural networks. IEEE Trans on Fuzzy Syst 9(4):578–594

    Article  Google Scholar 

  • Xu L, Krzyzak A, Oja E (1993) Penalized competitive learning for clustering analysis, RBF net, and curve detection. IEEE Trans Neural Networks 4:636–649

    Article  Google Scholar 

  • Yager RR, Filev DP (1993) Learning of fuzzy rules by mountain clustering. Proc SPIE Conf Applicat Fuzzy Logic Technol, Boston MA, pp 246–254

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  1. Faculty of Electrical Engineering, Tržaška 25, Ljubljana, Slovenia

    Dejan Dovžan & Igor Škrjanc

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  1. Dejan Dovžan
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  2. Igor Škrjanc
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Correspondence to Dejan Dovžan.

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Dovžan, D., Škrjanc, I. Recursive clustering based on a Gustafson–Kessel algorithm. Evolving Systems 2, 15–24 (2011). https://doi.org/10.1007/s12530-010-9025-7

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