On Sequential Cluster Extraction Based on L1-Regularized Possibilistic c-Means
Yukihiro Hamasuna* and Yasunori Endo**
*Department of Informatics, School of Science and Engineering, Kindai University
3-4-1 Kowakae, Higashi-osaka, Osaka 577-8502, Japan
**Faculty of Engineering, Information and Systems, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hard c-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types of L1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.
-  A. K. Jain, “Data clustering: 50 years beyond K-means,” Pattern Recognition Letters, Vol.31, No.8, pp. 651-666, 2010.
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.
-  S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering,” Springer, Heidelberg, 2008.
-  R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, No.2, pp. 98-110, 1993.
-  R. N. Davé and R. Krishnapuram, “Robust clustering methods: A unified view,” IEEE Trans. on Fuzzy Systems, Vol.5, No.2, pp. 270-293, 1997.
-  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.
-  R. R. Yager and D. P. Filev, Approximate clustering via the mountain method, it IEEE Transactions on Systems, Man and Cybernetics, Vol. 2, No. 8, pp. 1279–1284, 1994
-  R. N. Davé, “Characterization and detection of noise in clustering,” Pattern Recognition Letters, Vol.12, No.11, pp. 657-664, 1991.
-  Y. Hamasuna and Y. Endo, “Sequential Extraction By Using Two Types of Crisp Possibilistic Clustering,” Proc. of the IEEE Int. Conf. on Systems, Man, and Cybernetics (IEEE SMC 2013), pp. 3505-3510, 2013.
-  R. Inokuchi and S. Miyamoto, “Sparse Possibilistic Clustering with L1 Regularization,” Proc. of the 2007 IEEE Int. Conf. on Granular Computing (GrC2007), pp. 442-445, 2007.
-  K. Tsuda and T. Kudo, “Clustering graphs by weighted substructure mining,” Proc. of the 23rd Int. Conf. on Machine learning, pp. 953-960, 2006.
-  W. M. Rand, “Objective criteria for the evaluation of clustering methods,” J. of the American Statistical Association, Vol.66, No.336, pp. 846-850, 1971.