Rough Fuzzy K-Means Clustering Based on Parametric Decision-Theoretic Shadowed Set with Three-Way Approximation

Abstract

Rough fuzzy K-means (RFKM) decomposes data into clusters using partial memberships by underlying structure of incomplete information, which emphasizes the uncertainty of objects located in cluster boundary. In this scheme, the settings of cluster boundary merely depend on subjective judgment of perceptual experience. When confronted with the data exhibiting heavily overlap and imbalance, the boundary regions obtained by existing empirical schemes vary greatly accompanied by skewing of cluster center, which exerts considerable influence on the accuracy and stability of RFKM. This paper seeks to analyze and address this deficiency and then proposes an improved rough fuzzy K-means clustering based on parametric decision-theoretic shadowed set (RFKM-DTSS). Three-way approximation is implemented by incorporating a novel fuzzy entropy into the decision-theoretic shadowed set, which rationalizes cluster boundary through minimizing fuzzy entropy loss. Under the secondary adjustment method and improved update strategy of cluster center, the proposed RFKM-DTSS is thus featured by a powerful processing ability on class overlap and imbalance commonly seen in scenarios, such as fault detection and medical diagnosis with unclear decision boundaries. The effectiveness and robustness of the RFKM-DTSS are verified by the results of comparative experiments, demonstrating the superiority of the proposed algorithm.