Rough Set-Based Clustering Utilizing Probabilistic Memberships

Abstract

Representing the positive, possible, and boundary regions of clusters, rough set-based C-means clustering methods, such as generalized rough C-means (GRCM) and rough set C-means (RSCM), are promising for analyzing vague cluster shapes and realizing reliable classification. In this study, we consider rough set-based clustering approaches that utilize probabilistic memberships as variants of GRCM and RSCM, including π generalized rough C-means (πGRCM), π rough set C-means (πRSCM), and rough membership C-means (RMCM). πGRCM and πRSCM assign equal probabilities of cluster belonging according to Laplace’s principle of indifference, whereas RMCM assigns the probabilities according to rough memberships, which represent conditional probabilities based on the object’s neighborhood derived from a binary relation. In addition, we discuss the theoretical validity of our RMCM approach and compare it with other methods considered in this study. Furthermore, we conducted numerical experiments for evaluating the classification performances of the abovementioned methods. Based on our experimental results, the methods were found to be effective.