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Fuzzy Rule Extraction Using Radial Basis Function Neural Networks in High-Dimensional Data

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Intelligent Knowledge-Based Systems

Abstract

Rule learning is an increasingly important topic in both machine learning and data mining research. Machine learning concerns the development of algorithms or programs, which learn knowledge or skills while data mining is about the discovery of patterns or rules hidden in the data. Given a set of corresponding input-output values of a system, the challenge consists of identifying and formulating the relations between the input-output values in order to describe the system. To identify such relations, a functional input-output description may be provided. However, when dealing with complex processes, this is generally not feasible. One needs to look for alternative methods. The use of fuzzy models described through fuzzy rules has proven to be successful. Indeed, general knowledge about actions or conclusions can be expressed by a set of fuzzy If-Then rules of a Fuzzy Inference System (FIS).

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References

  1. J. S. Roger Jang, and C. T. Sun, Functional Equivalence Between Radial Basis Function Networks and Fuzzy Inference Systems, IEEE Transactions on Neural Networks, 4 (1) (1993) 156–158.

    Article  Google Scholar 

  2. R. T. Yager, and D. P Filev, Unified Structure and Parameter Identification of Fuzzy Models, IEEE Transactions on System Man and Cybernetics, 23 (1993) 1198–1205

    Article  Google Scholar 

  3. J. Nie, and D. A. Linkens, Learning Control Using Fuzzified Self-Organizing Radial Basis Function Network, IEEE Transactions on Fuzzy Systems, 1(4) (1993) 280–287.

    Article  Google Scholar 

  4. C. F. Juang, and C. T. Lin, An On-Line Self-Constructing Neural Fuzzy Inference Network and its Applications, IEEE Transactions on Fuzzy Systems, 6(1) (1998) 12–32.

    Article  Google Scholar 

  5. F. Klaw, and R. Kruse, Constructing a Fuzzy Controller from Data, Fuzzy Sets and Systems, 85 (1997) 177–193.

    Article  MathSciNet  Google Scholar 

  6. K. M. Lee, D. H. Kwak, and H. Leekwang, Tuning of Fuzzy Models by Fuzzy Neural Networks, Fuzzy Sets and Systems, 76 (1) (1995) 47–63.

    Article  MathSciNet  Google Scholar 

  7. Z. Q. Liu, and F. Yan, Fuzzy Neural Network in Case-Based Diagnostic System, IEEE Transactions on Fuzzy Systems, 5 (2) (1997) 209–222.

    Article  Google Scholar 

  8. T. Takagi and M. Sugeno, Fuzzy Identification of Systems and its Applications to Modeling and Control, IEEE Transactions on System Man and Cybernetics, (15) (1985) 116–132.

    Google Scholar 

  9. M. Delgado, A. F. Gomez-Skarmeta, and F. Martin, A Fuzzy Clustering-Based Rapid Prototyping for Fuzzy Rule-Based Modeling, IEEE Transactions on Fuzzy Systems, 5(2) (1997) 223–233.

    Article  Google Scholar 

  10. S. J. Raudys, and A. K. Jain, Small Sample Size Effects in Statistical Pattern Recognition: Recommendations for Practitioners, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13 (3) (1991) 252–264.

    Article  Google Scholar 

  11. M. Ramze Rezaee, B. Goedhart, B. P F. Lelieveldt, and J. H. C. Reiber, Fuzzy Feature Selection, Pattern Recognition 32 (1999) 2011–2019.

    Article  Google Scholar 

  12. D. S.Broomhead, and D. Lowe, Multivariable Function Interpolation and Adaptive Networks, Complex Systems, 2 (1988) 321–355.

    MATH  MathSciNet  Google Scholar 

  13. S. Chen, C. F. N. Cowan, and P M. Grant, Orthogonal Least Square Learning Algorithm for Radial Basis Function Networks, IEEE Transaction on Neural Networks, 2(2) (1991) 302–309.

    Article  Google Scholar 

  14. Y.S. Hwang and S. Y. Bang, An Efficient Method to Construct a Radial Basis Function Neural Network Classifier, Neural Networks, 10(8) (1997) 1495–1503.

    Article  Google Scholar 

  15. M. J. D. Powell, Radial Basis Functions Approximations to Polynomials, Proceeding of 12th Biennial Numerical Analysis Conference, Dundee, 1987, pp. 223–241.

    Google Scholar 

  16. B. Mulgrew, Applying Radial Basis Functions, IEEE Signal Processing Magazine, (1996) 50–64.

    Google Scholar 

  17. M. Musavi, W Ahmed, K. Chan, K. Faris and D. Hummels, On the Training ofRadial Basis Function Classifiers, Neural Networks, 5(4) (1992), 595–603.

    Article  Google Scholar 

  18. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum, (1981).

    MATH  Google Scholar 

  19. S. Abe, and R. Thawonmas, A Fuzzy Classifier with Elliptical Regions, IEEE Transactions on Fuzzy Systems, 5 (1997) 358–368.

    Article  Google Scholar 

  20. S. Abe, R. Thawnmas, and M. Kayama, A fuzzy Classifier with Ellipsoidal Regions for Diagnosis Problems, IEEE Transactions on System Man and Cybernetics, part C: Application and Reviews, 29(1) (1999) 140–149.

    Article  Google Scholar 

  21. M. S. Yang, Convergence Properties of the Generalised Fuzzy-C-Means Clustering Algorithms, Computers & Mathematics with Applications, 25(12) (1993) 3–11.

    Article  MATH  MathSciNet  Google Scholar 

  22. I. Gath, and A. B. Geva, Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7) (1989) 773–781.

    Article  Google Scholar 

  23. R. N. Davé, and R. Krishnapuram, Robust Clustering Methods: A Unified View, IEEE Transactions on Fuzzy Systems, 5(2) (1997) 270–293.

    Article  Google Scholar 

  24. L. Bobrowski, and J. C. Bezedek, C-Means Clustering with the Ll and L∞ Norms, IEEE Transactons on System Man and Cybernetics, 21(3) (1991) 545–554.

    Article  MATH  Google Scholar 

  25. P J. Rousseeuw, L. Kaufma, and E. Trauwaert, Fuzzy Clustering Using Scatter Matrices, Computational Statistics & Data Analysis, 23 (1996) 135–151.

    Article  MATH  Google Scholar 

  26. D. E. Gustafson, and W C. Kessel, Fuzzy Clustering with a Fuzzy Covariance Matrix, IEEE CDC, San Diego, (1979) 761–766.

    Google Scholar 

  27. P J. Rousseeuw, E. Trauwaert, and L. Kaufma, Fuzzy Clustering with High Contrast, Journal of Computational and Applied Mathematics 64 (1995) 81–90.

    Article  MATH  MathSciNet  Google Scholar 

  28. I. Gath, and A. B. Geva, Fuzzy Clustering for the Estimation of the Parameters of the Components of Mixtures of Normal Distributions, Pattern Recognition Letters, 9 (1989) 77–86.

    Article  MATH  Google Scholar 

  29. R. N. Davé, and R. Krishnapuram, Robust Clustering Methods: a Unified View, IEEE Transactions on Fuzzy Systems, 5(2) (1997) 270–293.

    Article  Google Scholar 

  30. E. Trauwaert, L. Kaufman, and P Rousseeuw, Fuzzy Clustering Algorithms based on the Maximum Likelihood Principle, Fuzzy Sets and Systems 42 (1991) 213–227.

    Article  MATH  Google Scholar 

  31. Y. Hamamoto, Y. Fujimoto, and S. Tomita, On the Estimation of a Covariance Matrix in Designing Parzen Classifiers, Pattern Recognition, 29 (10) (1996) 1751–1759.

    Article  Google Scholar 

  32. J. V. Ness, On the Dominance of Non-Parametric Bayes Rule Discriminant Algorithms in High Dimensions, Pattern Recognition 12 (1988) 355–368.

    Article  Google Scholar 

  33. F. Kimura, K. Takashima, S. Tsuruoka, and Y. Miyake, Modified Quadratic Discriminant Functions and the Application to Character Recognition, IEEE Transaction on Pattern Analysis and Machine Intelligence, 9(1) (1987) 149–153.

    Article  Google Scholar 

  34. K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, New York, 1990.

    MATH  Google Scholar 

  35. X. L. Xie, and G. A. Beni, Validity Measure for Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(8) (1991), 841–846.

    Article  Google Scholar 

  36. R. P Nikhil, and J. C. Bezdek, On Cluster Validity for the Fuzzy C-Means Model, IEEE Transactions on Fuzzy Systems 3(3) (1995) 370–379.

    Article  Google Scholar 

  37. M. Ramze Rezaee, B. P F. Lelieveldt, and J. H. C. Reiber, A New Cluster Validity Index for the Fuzzy C-Mean, Pattern Recognition Letters 19 (1998) 237–246.

    Article  MATH  Google Scholar 

  38. N. R. Pal, and J. C. Bezdek, On Cluster Validity for Fuzzy c-Means Model, IEEE Transactions on Fuzzy Systems 3(3) (1995) 370–379.

    Article  Google Scholar 

  39. N. R. Pal, and J. C. Bezdek, Correction to on Cluster Validity for the Fuzzy-C-Means Model, IEEE Transactions on Fuzzy Systems, 5(1) (1997) 152–153.

    Article  Google Scholar 

  40. M. Kubat, Decision Trees can Initialize Radial Basis Function Networks, IEEE Transactions on Neural Networks 9(5) (1998) 813–821.

    Article  MathSciNet  Google Scholar 

  41. P Murphy, and D. Aha, “UCI Repository of Machine Learning Databases [machine-readable data respository],” Tech. Rep., Univ. Calif., Ivrine, CA. http:www.ics.uci.edu/AL/ML/Machine-Learning.html.

    Google Scholar 

  42. F. _Behloul, B. P F. Lelieveldt, A. Boudraa, and J. H. C. Reiber, “Optimal design of radial basis function neural networks fo fuzzy rule extraction in high dimensional data,” Pattern recognition, vol. 35, pp. 659–675, 2002.

    MATH  Google Scholar 

  43. D. Dubois and H. Padre. Fuzzy Sets and Systems: Theory and Applications. Academic Press, Inc, 1980.

    Google Scholar 

  44. L. A. Zadeh, “Fuzzy sets,” Information and Control, 1965, vol. 8, pp. 333–353.

    Article  MathSciNet  Google Scholar 

  45. J. S. R. Jang, “ANFIS: Adaptive-Network-based Fuzzy Inference Systems,” IEEE Transactions on Systems, Man and Cybernetics, 1993, vol. 23, no. 3, pp. 665–685.

    Article  MathSciNet  Google Scholar 

  46. J. Moody and C. Darken, “Fast learning in networks of locally-tuned processing units,” Neural Computations, 1989, vol. 1, pp. 281–294.

    Article  Google Scholar 

  47. Z.-Q. Liu and F. Van, “Fuzzy neural network in case-based diagnostic system,” IEEE Transactions on Fuzzy Systems, 1997, vol. 5, no. 2, pp. 209–222.

    Article  Google Scholar 

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Admiraal-Behloul, F., Reiber, J.H.C. (2005). Fuzzy Rule Extraction Using Radial Basis Function Neural Networks in High-Dimensional Data. In: Leondes, C.T. (eds) Intelligent Knowledge-Based Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-7829-3_44

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  • DOI: https://doi.org/10.1007/978-1-4020-7829-3_44

  • Publisher Name: Springer, Boston, MA

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  • Online ISBN: 978-1-4020-7829-3

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