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A fuzzy clustering algorithm enhancing local model interpretability

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Abstract

In this work, simple modifications on the cost index of particular local-model fuzzy clustering algorithms are proposed in order to improve the readability of the resulting models. The final goal is simultaneously providing local linear models (reasonably close to the plant’s Jacobian) and clustering in the input space so that desirable characteristics (regarding final model accuracy, and convexity and smoothness of the cluster membership functions) are improved with respect to other proposals in literature. Some examples illustrate the proposed approach.

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References

  • Ahvenlampi T, Díez JL, Navarro JL (2003) New methods for validation of local models in fuzzy clustering identification. In: Proceedings of IFAC conference on intelligent control and signal processing, pp 9–12, Elsevier, Oxford

  • Angelov P, Xydeas C (2006) Fuzzy systems design: direct and indirect approaches. Soft comput 10:836–849

    Article  Google Scholar 

  • Babuska R (1998) Fuzzy modeling for control. Kluwer, Boston

    Google Scholar 

  • Babuska R, Fantuzzi C, Verbruggen HB (1996) Improved inference for takagi-sugeno models. In: Proceedings IEEE conference on fuzzy systems, New Orleans, pp 653–664

  • Babuska R, van der Veen PJ, Kaymak U (2002) Improved covariance estimation for gustafson-kessel clustering. In: Proceedings IEEE conference on fuzzy systems, Honolulu

  • Baptistella LFB, Ollero A (1980) Fuzzy methodologies for interactive multicriteria optimmization. IEEE Trans Syst, Man Cybern 10:355–365

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas DP (1999) Nonlinear programming. Springer, London

    MATH  Google Scholar 

  • Bezdek JC (1987) Pattern recognition with fuzzy objective function algorithms. Plenum, New York

    Google Scholar 

  • Davé RN (1991) Characterization and detection of noise clustering. Pattern Recogn Lett 12:657–664

    Article  Google Scholar 

  • Davé RN, Krishnapuram R (1997) Robust clustering methods: a unified view. IEEE Trans Fuzzy Syst 5:270–293

    Article  Google Scholar 

  • Díez JL, Navarro JL, Sala A (2001) Identification for local model control with fuzzy clustering. In: Proceedings IFAC workshop on advanced fuzzy-neural control, pp 99–104, Elsevier, Oxford

  • Díez JL, Sala A, Navarro JL (2006) Target-shape possibilistic clustering applied to local-model identification. Eng Appl Artif Intell 19:201–208

    Article  Google Scholar 

  • Duda RO, Hart PE, Stork DG (2000) Pattern classification. Wiley, New York

    Google Scholar 

  • Emami MR, Türksen IB, Goldenberg AA (1998) Development of a systematic methodology of fuzzy logic modeling. IEEE Trans Fuzzy Syst 6:346–366

    Article  Google Scholar 

  • Guillaume S (2001) Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans Fuzzy Syst 9:426–443

    Article  Google Scholar 

  • Gustafson EE, Kessel WC (1979) Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of IEEE CDC, San Diego, pp 761–766

  • Hathaway RJ, Bezdek JC (1993) Switching regression models and fuzzy clustering. IEEE Trans Fuzzy Syst 1:195–204

    Article  Google Scholar 

  • Johansen TA, Murray-Smith R (1997) The operating regime to nonlinear modelling and control. In: Murray-Smith R, Johansen TA (eds) Multiple model approaches to modelling and control. Taylor & Francis, London

    Google Scholar 

  • Johansen TA, Shorten R, Murray-Smith R (2000) On the interpretation and identification of dynamic takagi-sugeno fuzzy models. IEEE Trans Fuzzy Syst 8:297–313

    Article  Google Scholar 

  • Johansson R (1993) System modeling and identification. Prentice-Hall, Information and System Sciences series, New Jersey

    Google Scholar 

  • Krishnapuram R, Keller JM (1993) A possibilistic approach to clustering. IEEE Trans Fuzzy Syst 1:98–110

    Article  Google Scholar 

  • Lee S, Yen GE (2002) On the local interpretation of takagi-sugeno fuzzy models from a dynamical systems view. In: Proceedings of the American control conference, pp 519–524, Anchorage, Alaska

  • Ljung L (1999) System identification. Prentice-Hall, New Jersey

    Google Scholar 

  • Murray-Smith R, Johansen TA (1997) Local learning in local model networks. In: Murray-Smith R, Johansen TA (eds) Multiple model approaches to modelling and control. Taylor & Francis, London

    Google Scholar 

  • Nocedal J, Wright SJ (1999) Numerical optimization. Springer, London

    Book  MATH  Google Scholar 

  • Romero JA, Navarro JL, Bruno JM (2002) Estimación de parámetros del modelo de un biorreactor aplicando algoritmos genéticos. ITecnike Journal (in Spanish), Innovación e Investigación en la Ingeniería 2:31–34

    Google Scholar 

  • Ryoke M, Nakamori Y (1996) Simultaneous analysis of classification and regression by adaptive fuzzy clustering. Jpn J Fuzzy Theory Syst 8:99–113

    Google Scholar 

  • Sala A, Guerra TM, Babuska R (2005) Perspectives of fuzzy systems and control. Fuzzy Sets Syst 156:432–444

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Vemieuwe H, De Baets B, Verhoest NEC (2006) Comparison of clustering algorithms in the identification of takagi- sugeno models: a hydrological case study. Fuzzy Sets Syst 157: 2876–2896

    Article  Google Scholar 

  • Walter E, Pronzato L (1997) Identification of parametric models from experimental data. Springer, London

    MATH  Google Scholar 

  • Wang L-X (1997) A course in fuzzy systems and control. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  • Yen J, Wang L, Gillespie CW (1998) Improving the interpretability of tsk fuzzy models by combining global learning and local learning. IEEE Trans Fuzzy Syst 6:530–537

    Article  Google Scholar 

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Díez, J.L., Navarro, J.L. & Sala, A. A fuzzy clustering algorithm enhancing local model interpretability. Soft Comput 11, 973–983 (2007). https://doi.org/10.1007/s00500-006-0146-7

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