Convex-set-based fuzzy clustering

Prototype-based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a two-level fuzzy clustering method that involves adaptively expanding and merging convex polytopes, where the convex polytopes are considered as a “flexible” prototype. Therefore, the dependency on the use of a specified prototype can be eliminated. Also, the proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. In the first level of our proposed method, each cluster is represented by a convex polytope which is described by its set of vertices. Specifically, nonlinear membership functions are utilized to determine whether an input pattern creates a new cluster or whether an existing cluster should be modified. In the second level, the expandable clusters that are selected by an intercluster distance measure are merged to improve clustering efficiency and to reduce the order dependency of the incoming input patterns. Several experimental results are given to show the validity of our method.