OCCM-RPS: Ordered credal C-means clustering based on random permutation set

Evidential clustering has received extensive attention due to its ability to generate credal partitions that represent cluster-membership uncertainty. However, credal partitions based on mass functions can not reflect the propensity information between samples and clusters, and existing evidential clustering methods rarely incorporate attribute weights into distance functions. To address these two shortcomings, we introduce the Random Permutation Set (RPS) into evidential clustering frameworks for the first time, and propose a novel approach called Ordered Credal C-means clustering based on RPS (OCCM-RPS). Specifically, we first present an improved coefficient of variant to determine attribute weights in a simple and effective manner. Secondly, we introduced a new concept of ordered credal partition to depict clustering results, which can both quantitatively represent the cluster-membership uncertainty and qualitatively reflect the propensity of samples toward different clusters. Twelve well-known benchmark datasets and two synthetic datasets are employed to evaluate the effectiveness of OCCM-RPS, and experimental results show that the proposed OCCM-RPS can capture original characteristics of datasets more comprehensively using a higher-order form of data representation, and significantly improve the hard clustering performance compared with the state-of-the-art evidential clustering algorithms.