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Robust Clustering Algorithms Employing Fuzzy-Possibilistic Product Partition

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 671))

Abstract

One of the main challenges in the field of clustering is creating algorithms that are both accurate and robust. The fuzzy-possibilistic product partition c-means clustering algorithm was introduced with the main goal of producing accurate partitions in the presence of outlier data. This chapter presents several clustering algorithms based on the fuzzy-possibilistic product partition, specialized for the detection of clusters having various shapes including spherical and ellipsoidal shells. The advantages of applying the fuzzy-possibilistic product partition are presented in comparison with previous c-means clustering models. Besides being more robust and accurate than previous probabilistic-possibilistic mixture partitions, the product partition is easier to handle due to its reduced number of parameters.

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References

  1. Bezdek, J. C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)

    Google Scholar 

  2. Davé, R. N.: Characterization and detection of noise in clustering. Patt. Recogn. Lett. 12, 657–664 (1991)

    Google Scholar 

  3. Menard, M., Damko, C., Loonis, P.: The fuzzy \(c+2\) means: solving the ambiguity rejection in clustering. Patt. Recogn. 33, 1219–1237 (2000)

    Google Scholar 

  4. Chintalapudi, K. K., Kam, M.: A noise-resistant fuzzy \(c\)-means algorithm for clustering. IEEE World Congr. Comput. Intell. 1458–1463 (1998)

    Google Scholar 

  5. Alanzado, A. C., Miyamoto, S.: Fuzzy \(c\)-means clustering in the presence of noise cluster for time series analysis. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 3558, 156–163 (2005)

    Google Scholar 

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

    Google Scholar 

  7. Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996)

    Google Scholar 

  8. Timm, H., Borgelt, C., Döring, C., Kruse, R.: An extension to possibilistic fuzzy cluster analysis. Fuzzy Sets and Systems 147, 3–16 (2004)

    Google Scholar 

  9. Pal, N. R., Pal, K., Bezdek, J. C.: A mixed \(c\)-means clustering model. Proc. IEEE Int’l Conf. Fuzzy Systems (FUZZ-IEEE), pp. 11–21 (1997)

    Google Scholar 

  10. Pal, N. R., Pal, K., Keller, J. M., Bezdek, J. C.: A possibilistic fuzzy \(c\)-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13, 517–530 (2005)

    Google Scholar 

  11. Szilágyi, L.: Fuzzy-Possibilistic Product Partition: a novel robust approach to c-means clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 6820, 150–161 (2011)

    Google Scholar 

  12. Gunderson, R.: An adaptive FCV clustering algorithm. Int. J. Man-Mach. Stud. 19, 97–104 (1983)

    Google Scholar 

  13. Krishnapuram, R., Nasraoui, O., Frigui, H.: A fuzzy \(c\) spherical shells algorithm: a new approach. IEEE Trans. Neur. Netw. 3, 663–671 (1992)

    Google Scholar 

  14. Davé, R. N.: Generalized fuzzy \(c\)-shells clustering and detection of circular and elliptical boundaries. Pattern Recogn. 25(7), 713–721 (1992)

    Google Scholar 

  15. Frigui, H., Krishnapuram, R.: A comparison of fuzzy shell clustering methods for the detection of ellipses. IEEE Trans. Fuzzy Syst. 4, 193–199 (1996)

    Google Scholar 

  16. Krishnapuram, R., Frigui, H., Nasraoui, O.: New fuzzy shell clustering algorithms for boundary detection and pattern recognition. SPIE Proc. Robot. Comp. Vis. 1607, 1460–1465 (1991)

    Google Scholar 

  17. Davé, R. N., Bhaswan, K.: Adaptive fuzzy \(c\)-shells clustering and detection of ellipses. IEEE Trans. Neural Netw. 3(5), 643–662 (1992)

    Google Scholar 

  18. Krishnapuram, R., Frigui, H., Nasraoui, O.: Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation - Part I. IEEE Trans. Fuzzy Syst. 3, 29–43 (1995)

    Google Scholar 

  19. Bezdek, J.C., Hathaway, R.J., Pal, N.R.: Norm induced shell prototype (NISP) clustering. Neur. Parall. Sci. Comput. 3, 431–450 (1995)

    Google Scholar 

  20. Höppner, F.: Fuzzy shell clustering algorithms in image processing: fuzzy \(c\)-rectangular and 2-rectangular shells. IEEE Trans. Fuzzy Syst. 5, 599–613 (1997)

    Google Scholar 

  21. Steinhaus, H.: Sur la division des corp materiels en parties. Bull. Acad. Pol. Sci. C1 III. (IV) 801–804 (1956)

    Google Scholar 

  22. Szilágyi, L., Szilágyi, S. M., Benyó, B., Benyó, Z.: Intensity inhomogeneity compensation and segmentation of MR brain images using hybrid \(c\)-means clustering models. Biomed. Sign. Proc. Contr. 6, 3–12 (2011)

    Google Scholar 

  23. Szilágyi, L.: Robust spherical shell clustering using fuzzy-possibilistic product partition. Int. J. Intell. Syst. 28, 524–539 (2013)

    Google Scholar 

  24. Szilágyi, L., Varga, Zs. R., Szilágyi, S. M.: Application of the fuzzy-possibilistic product partition in elliptic shell clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 8825, 158–169 (2014)

    Google Scholar 

  25. Anderson, E.: The IRISes of the Gaspe peninsula. Bull. Amer. IRIS Soc. 59, 2–5 (1935)

    Google Scholar 

  26. Gosztolya, G., Szilágyi, L.: Application of fuzzy and possibilistic \(c\)-means clustering models in blind speaker clustering. Acta Polytech. Hung. 12(7), 41–56 (2015)

    Google Scholar 

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Szilágyi, L. (2017). Robust Clustering Algorithms Employing Fuzzy-Possibilistic Product Partition. In: Torra, V., Dahlbom, A., Narukawa, Y. (eds) Fuzzy Sets, Rough Sets, Multisets and Clustering. Studies in Computational Intelligence, vol 671. Springer, Cham. https://doi.org/10.1007/978-3-319-47557-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-47557-8_7

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