FCMBased Model Selection Algorithms for Determining the Number

FCM-Based Model Selection Algorithms for Determining the Number of Clusters Haojun Sun, Shengrui. Wang*, Qingshan Jiang Received 16 December 2002; received in revised form 29 March 2004; accepted 29 March 2004 Presenter Chia-Cheng Chen 1

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

Introduction 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

Basic algorithm FCM algorithm 4

Basic algorithm(Cont. ) 5

Basic algorithm(Cont. ) FCM-based model selection algorithm 6

Basic algorithm(Cont. ) FBSA: FCM-Based Splitting Algorithm 7

Basic algorithm(Cont. ) Function S(i) 8

A new validity index 9

A new validity index(Cont. ) 10

Experimental results Data. Set 1 ◦ IRIS data ◦ This is a biometric data set consisting of 150 measurements belonging to three flower varieties Data. Set 2 ◦ Mixture of Gaussian distributions ◦ 50 data vectors in each of the 5 ve clusters Data. Set 3 ◦ Mixture of Gaussian distributions ◦ 500 data vectors 11

Experimental results(Cont. ) 12

Experimental results(Cont. ) 13

Experimental results(Cont. ) 14

Experimental results(Cont. ) 15

Experimental results(Cont. ) 16

Experimental results(Cont. ) 17

Conclusion and perspectives 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