Sequential Cluster Extraction Using Power-Regularized Possibilistic c-Means
Shibaura Institute of Technology, 3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan
The present study proposes an algorithm for sequential cluster extraction using power-regularized possibilistic c-means (pPCM). First, pPCM is derived in a similar manner to two types of entropy-regularized possibilistic c-means (ePCM) derivations, where a power function is utilized instead of the negative entropy in ePCM. The cluster fusion with pPCM is identical to the mean-shift with a generalized Epanichnikov kernel, whereas the proposed method employs sequential cluster extraction with pPCM. Numerical examples show that the cluster number produced by the proposed algorithm did not match with the true class number in real datasets, but the extracted clustering results were partially successful in terms of capturing dense regions of objects.
-  J. B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations,” Proc. 5th Berkeley Symp. on Math. Stat. and Prob., pp. 281-297, 1967.
-  J. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.
-  S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a Regularization and Maximum Entropy Approach,” Proc. 7th Int. Fuzzy Systems Association World Congress (IFSA1997), Vol.2, pp. 86-92, 1997.
-  S. Miyamoto and K. Umayahara, “Fuzzy Clustering by Quadratic Regularization,” Proc. 1998 IEEE Int. Conf. Fuzzy Syst., pp. 1394-1399, 1998.
-  Y. Kanzawa, “Generalization of Quadratic Regularized and Standard Fuzzy c-Means Clustering with respect to Regularization of Hard c-Means,” LNCS, Vol.8234, pp. 152-165, 2013.
-  R. Krishnapuram and J. M. Keller, “A Possibilistic Approach to Clustering,” IEEE Trans. Fuzzy Syst., Vol.1, pp. 98-110, 1993.
-  R. Krishnapuram and J. M. Keller, “The Possibilistic c-Means Algorithm: Insights and Recommendations,” IEEE Trans. Fuzzy Syst., Vol. 4, pp. 393-396, 1996.
-  S. Miyamoto, R. Inokuchi, and Y. Kuroda, “Possibilistic and Fuzzy c-Means Clustering with Weighted Objects,” Proc. 2006 IEEE Int. Conf. on Fuzzy Systems, pp. 869-874, 2006.
-  S. Miyamoto, Y. Kuroda, and K. Arai, “Algorithms for Sequential Extraction of Clusters by Possibilistic Method and Comparison with Mountain Clustering,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.12, No.5, pp. 448-453, 2008.
-  K. Fukunaga and L. D. Hostetler, “The Estimation of the Gradient of a Density Function with Applications in Pattern Recognition,” IEEE Trans. Inf. Theory, Vol.21, pp. 32-40, 1975.
-  Y. Hamasuna and Y. Endo, “On sparse possibilistic clustering with crispness – Classification function and sequential extraction,” Proc. Soft Computing and Intelligent Systems (SCIS) and 13th Int. Symp. on Advanced Intelligent Systems (ISIS), 2012 Joint 6th Int. Conf., pp. 1801-1806, 2012.
-  K.-L. Wu and M.-S. Yang, “Mean shift-based clustering,” Pattern Recognit., Vol.40, No.11, pp. 3035-3052, 2007.
-  C. L. Blake and C. J. Merz, “UCI repository of machine learning databases, a huge collection of artificial and real-world data sets,” 1998, available at:
http://archive.ics.uci.edu/ml/ [Accessed April 20, 2014]