BE-ECM: Belief Entropy-based Evidential C-Means and its application in data clustering

Abstract

As an extension of Fuzzy C-Means based on Dempster-Shafer evidence theory, Evidential C-Means (ECM) generalizes fuzzy partition to credal partition and has been widely applied. However, ECM’s objective function only considers distortion between objects and prototypes, making it highly sensitive to prototype initialization and prone to the local optima problem. While maximum entropy-based methods improve stability by entropy regularization, they are limited to fuzzy partition and cannot handle credal partition with multi-class uncertainty in evidential clustering. To overcome the issues, this paper proposes Belief Entropy-based Evidential C-Means (BE-ECM), which uniquely equips ECM with a belief entropy-based Maximum Entropy Principle (MEP) framework. Compared to ECM, BE-ECM considers not only the distortion term but also a negative belief entropy term, leveraging MEP to enhance stability against the local optimal problem. Unlike other maximum entropy-based methods, BE-ECM incorporates credal partition with belief entropy, enabling explicit multi-class uncertainty modeling and stable evidential clustering. During the clustering process of BE-ECM, the negative belief entropy term initially dominates to provide unbiased estimation for unknown data distributions, mitigating the impact of poorly initialized prototypes and reducing the risks of local optima, while the distortion term gradually refines the credal partition as clustering progresses. Experimental results demonstrate BE-ECM’s superior performance and high stability on clustering tasks compared with the existing clustering algorithms.