Agglomerative Learning Algorithms for General Fuzzy Min-Max Neural Network

  • Bogdan Gabrys
Article

Abstract

In this paper two agglomerative learning algorithms based on new similarity measures defined for hyperbox fuzzy sets are proposed. They are presented in a context of clustering and classification problems tackled using a general fuzzy min-max (GFMM) neural network. The proposed agglomerative schemes have shown robust behaviour in presence of noise and outliers and insensitivity to the order of training patterns presentation. The emphasis is also put on the complimentary features to the previously presented incremental learning scheme more suitable for on-line adaptation and dealing with large training data sets. The performance and other properties of the agglomerative schemes are illustrated using a number of artificial and real-world data sets.

pattern classification hierarchical clustering agglomerative learning neuro-fuzzy system hyperbox fuzzy sets 

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References

  1. 1.
    M.H. Hassoun, Fundamentals of Artificial Neural Networks, Cambridge, MA: The MIT Press, 1995.MATHGoogle Scholar
  2. 2.
    S. Mitra and K. Pal, “Self-Organizing Neural Network As a Fuzzy Classifier,” IEEE Trans. on Systems, Man and Cybernetics, vol. 24,no. 3, 1994.Google Scholar
  3. 3.
    W. Pedrycz, “Fuzzy Neural Networks with Reference Neurons as Pattern Classifiers,” IEEE Trans. on Neural Networks, vol. 3,no. 5, 1992.Google Scholar
  4. 4.
    P.K. Simpson, “Fuzzy Min-Max Neural Networks—Part 1: Classification,” IEEE Trans. on Neural Networks, vol. 3,no. 5, 1992, pp. 776-786.CrossRefGoogle Scholar
  5. 5.
    P.K. Simpson, “Fuzzy Min-Max Neural Networks—Part 2: Clustering,” IEEE Trans. on Fuzzy Systems, vol. 1,no. 1, 1993, pp. 32-45.CrossRefGoogle Scholar
  6. 6.
    R.R. Yager and L.A. Zadeh (Eds.), Fuzzy Sets, Neural Networks, and Soft Computing, Van Nostrand Reinhold, 1994.Google Scholar
  7. 7.
    B. Gabrys, “Data Editing for Neuro Fuzzy Classifiers,” in Proceedings of the SOCO'2001 Conference, Paisley, UK, 2001.Google Scholar
  8. 8.
    B. Gabrys, “Pattern Classification for Incomplete Data,” in Proceedings of 4th International Conference on Knowledge-Based Intelligent Engineering Systems & Allied Technologies KES'2000, Brighton, vol. 1, 2000, pp. 454-457.Google Scholar
  9. 9.
    B. Gabrys and A. Bargiela, “Neural Networks Based Decision Support in Presence of Uncertainties,” J. of Water Resources Planning and Management, vol. 125,no. 5, 1999, pp. 272-280.CrossRefGoogle Scholar
  10. 10.
    B. Gabrys and A. Bargiela, “General Fuzzy Min-Max Neural Network for Clustering and Classification,” IEEE Trans. on Neural Networks, vol. 11,no. 3, 2000, pp. 769-783.CrossRefGoogle Scholar
  11. 11.
    J. Boberg and T. Salakoski, “General Formulation and Evaluation of Agglomerative Clustering Methods with Metric and Non-metric Distances,” Pattern Recognition, vol. 26,no. 9, 1993, pp. 1395-1406.CrossRefGoogle Scholar
  12. 12.
    H. Frigui and R. Krishnapuram, “Clustering by Competitive Agglomeration,” Pattern Recognition, vol. 30,no. 7, 1997, pp. 1109-1119.CrossRefGoogle Scholar
  13. 13.
    H. Frigui and R. Krishnapuram, “A Robust Competitive Clustering Algorithm with Applications in Computer Vision,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 21,no. 5, 1999, pp. 450-465.CrossRefGoogle Scholar
  14. 14.
    S. Theodoridis and K. Koutroumbas, Pattern Recognition, San Diego, CA: Academic Press, 1999.Google Scholar
  15. 15.
    K. Ozawa, “Classic: A Hierarchical Clustering Algorithm Based on Asymetric Similarities,” Pattern Recognition, vol. 16,no. 2, 1983, pp. 201-211.CrossRefMATHGoogle Scholar
  16. 16.
    L.I. Kuncheva, Fuzzy Classifier Design, Heidelberg: Physica-Verlag, 2000.CrossRefMATHGoogle Scholar
  17. 17.
    B.D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, 1996.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Bogdan Gabrys
    • 1
  1. 1.Applied Computational Intelligence Research Unit, Division of Computing and Information SystemsUniversity of PaisleyPaisleyScotland, UK

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