Cumulative belief peaks evidential K-nearest neighbor clustering

Abstract

This paper introduces a new evidential clustering algorithm based on finding the “cumulative belief peaks” and evidential K-nearest neighbor rule. The basic assumption of this algorithm is that a cluster center has the highest cumulative possibility of becoming a cluster center among its neighborhood and size of its neighborhood is relatively large. To measure such cumulative possibility, a new notion of cumulative belief is proposed in the framework of belief functions. By maximizing an objective function, an appropriate size of the relatively large neighborhood is determined. Then, the objects with highest cumulative belief among their own neighborhood of this size are automatically detected as cluster centers. Finally, a credal partition is derived by evidential K-nearest neighbor rule with the fixed cluster center. Experimental results show that the proposed evidential clustering algorithm can automatically detect cluster centers and well reveal the data structure in form of a credal partition in tolerable time, when tackling datasets with small number of data objects and dimensions. As the sizes of datasets increase, running time of such new clustering algorithm increases sharply and this reduces the practicability of it. Simulations on synthetic and real-world datasets validate our conclusions.