Fuzzy Clustering with New Separable Criterion

Fuzzy clustering has been used widely in education, statistics, engineering, communication...etc. The fuzzy partition clustering algorithms are most based on Euclidean distance function, which can only be used to detect spherical structural clusters. Extending Euclidean distance to Mahalanobis distance, GustafsonKessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect nonspherical structural clusters, but these two algorithms fail to consider the relationships between cluster centers in the objective function. Yin-Tang-Sun-Sun (YTSS) clustering algorithm solved the relationships between cluster centers question, unfortunately, they did not consider the distance between the center of all data points and the center of each cluster. This problem was solved and presented in this paper. In this paper, a new fuzzy clustering algorithm (LWM) was developed based on the conventional fuzzy cmeans (FCM) to obtain better quality clustering results with new separable criterion and better initial value. It is different from YTSS cluster algorithm. The improved equations for the membership and the cluster center were derived from the alternating optimization algorithm. Ten fuzzy scattering matrices in the objective function assure the compactness between data points and cluster centers, and also strengthen the separation between cluster centers in terms of a new separable criterion. The conclusions were drawn from this study as follows. (a) The distance between the center of all points and the center of each cluster was considered to obtain more accurate clustering results. (b) The singular problem was solved by using LWM algorithm. (c) The β value would not be required. The β value could be replaced by the best value, produced by the new LWM algorithm, developed by the authors of this paper. (d) Numerical data show that the LWM clustering algorithm gave more accurate clustering results than the FCM and YTSS clustering algorithm. Key-Words: GG clustering algorithm, GK clustering algorithm, YTSS clustering algorithm. WSEAS TRANSACTIONS on BIOLOGY and BIOMEDICINE Hsiang-Chuan Liu, Der-Bang Wu, Hsiu-Lan Ma ISSN: 1109-9518 99 Issue 7, Volume 4, July 2007