Un Co Rr Ec Te D Pr Oo F Pr 1602 Article in Press

7 Major problems exist in both crisp and fuzzy clustering algorithms. The fuzzy c-means type of algorithms use weights determined by a power m of inverse distances that remains 0xed over all iterations and over all clusters, even though smaller 9 clusters should have a larger m. Our method uses a di4erent “distance” for each cluster that changes over the early iterations to 0t the clusters. Comparisons show improved results. We also address other perplexing problems in clustering: (i) 0nd the 11 optimal number K of clusters; (ii) assess the validity of a given clustering; (iii) prevent the selection of seed vectors as initial prototypes from a4ecting the clustering; (iv) prevent the order of merging from a4ecting the clustering; and (v) permit the 13 clusters to form more natural shapes rather than forcing them into normed balls of the distance function. We employ a relatively large number K of uniformly randomly distributed seeds and then thin them to leave fewer uniformly distributed seeds. Next, 15 the main loop iterates by assigning the feature vectors and computing new fuzzy prototypes. Our fuzzy merging then merges any clusters that are too close to each other. We use a modi0ed Xie-Bene validity measure as the goodness of clustering 17 measure for multiple values of K in a user-interaction approach where the user selects two parameters (for eliminating clusters and merging clusters after viewing the results thus far). The algorithm is compared with the fuzzy c-means on the iris data 19 and on the Wisconsin breast cancer data. ? 2002 Published by Elsevier Science Ltd on behalf of Pattern Recognition Society.