Credal c-means clustering method based on belief functions

Abstract

The recent credal partition approach allows the objects to belong to not only the singleton clusters but also the sets of clusters (i.e. meta-clusters) with different masses of belief. A new credal c-means (CCM) clustering method working with credal partition has been proposed in this work to effectively deal with the uncertain and imprecise data. In the clustering problem, one object simultaneously close to several clusters can be difficult to correctly classify, since these close clusters appear not very distinguishable for this object. In such case, the object will be cautiously committed by CCM to a meta-cluster (i.e. the disjunction of these close clusters), which can be considered as a transition cluster among these different close clusters. It can well characterize the imprecision of the class of the object and can also reduce the misclassification errors thanks to the use of meta-cluster. CCM is robust to the noisy data because of the outlier cluster. The clustering centers and the mass of belief on each cluster for any object are obtained by the optimization of a proper objective function in CCM. The effectiveness of CCM has been demonstrated by three experiments using synthetic and real data sets with respect to fuzzy c-means (FCM) and evidential c-means (ECM) clustering methods.