ECM+: An improved evidential c-means with adaptive distance

Evidential c-means (ECM) is a prototype-based clustering algorithm that generates a credal partition. Such a partition encompasses the notions that can be encountered with a hard, fuzzy or possibilistic partition, allowing the representation of various situations concerning the class membership of an object. The ECM method provides a prototype for each subset of the possible classes, calculated by averaging the prototypes of the classes included in the subsets. Although this definition perfectly suits ECM when employing a Euclidean distance, it becomes inappropriate when using a Mahalanobis distance. In this context, a new definition of prototypes for the subsets is proposed. The ECM objective function is then optimized using the new definition of prototypes. The subsequent algorithm, named ECM+, is finally tested on various synthetic and real data sets to demonstrate its interest compared to ECM.