A new evidential c-means clustering method

Data clustering methods integrating information fusion techniques have been recently developed in the framework of belief functions. More precisely, the evidential version of fuzzy c-means (ECM) method has been proposed to deal with the clustering of proximity data based on an extension of the popular fuzzy c-means (FCM) clustering method. In fact ECM doesn´t perform very well for proximity data because it is based only on the distance between the object and the clusters´ center to determine the mass of belief of the object commitment. As a result, different clusters can overlap with close centers which is not very efficient for data clustering. To overcome this problem, we propose a new clustering method called belief functions c-means (BFCM) in this work. In BFCM, both the distance between the object and the imprecise cluster´s center, and the distances between the object and the centers of the involved specific clusters for the mass determination are taken into account. The object will be considered belonging to a specific cluster if it is very close to this cluster´s center, or belonging to an imprecise cluster if it lies in the middle (overlapped zone) of some specific clusters, or belonging to the outlier cluster if it is too far from the data set. Pignistic probability can be applied for the hard decision making support in BFCM. Several examples are given to illustrate how BFCM works, and to show how it outperforms ECM and FCM for the proximity data.