ECMdd: Evidential c-medoids clustering with multiple prototypes

• Extend medoid-based clustering algorithm on the framework of belief functions.
• Introduce imprecise clusters which enable us to make soft decisions for uncertain data.
• Use multiple weighted prototypes to capture various types of class structure.
• Experimental results confirm the superiority of the proposed clustering algorithms.

In this work, a new prototype-based clustering method named Evidential C-Medoids (ECMdd), which belongs to the family of medoid-based clustering for proximity data, is proposed as an extension of Fuzzy C-Medoids (FCMdd) on the theoretical framework of belief functions. In the application of FCMdd and original ECMdd, a single medoid (prototype), which is supposed to belong to the object set, is utilized to represent one class. For the sake of clarity, this kind of ECMdd using a single medoid is denoted by sECMdd. In real clustering applications, using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance. In order to address this problem, a variation of ECMdd using multiple weighted medoids, denoted by wECMdd, is presented. Unlike sECMdd, in wECMdd objects in each cluster carry various weights describing their degree of representativeness for that class. This mechanism enables each class to be represented by more than one object. Experimental results in synthetic and real data sets clearly demonstrate the superiority of sECMdd and wECMdd. Moreover, the clustering results by wECMdd can provide richer information for the inner structure of the detected classes with the help of prototype weights.