Haojun Sun,ShengruiWang*,Qingshan Jiang Received 16 December 2002; received in revised form 29 March 2004; accepted 29 March 2004 Presenter Chia-Cheng Chen 1

 Introduction  Basic algorithm  A new validity index  Experimental results  Conclusion and perspectives 2

 Clustering is a process for grouping a set of objects into classes or clusters so that the objects within a cluster have high similarity.  Because of its concept of fuzzy membership, FCM is able to deal more effectively with outliers and to perform membership grading, which is very important in practice. 3

 FCM algorithm 4

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 FCM-based model selection algorithm 6

 FBSA: FCM-Based Splitting Algorithm 7

 Function S(i) 8

 A new validity index 9

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 DataSet1 ◦ IRIS data ◦ This is a biometric data set consisting of 150 measurements belonging to three flower varieties  DataSet2 ◦ Mixture of Gaussian distributions ◦ 50 data vectors in each of the 5ve clusters  DataSet3 ◦ Mixture of Gaussian distributions ◦ 500 data vectors 11

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 The major contributions of this paper are an improved FCM-based algorithm for determining the number of clusters and a new index for validating clustering results.  Use of the new algorithm to deal with the dimension reduction problem is another promising avenue. 18