Objective function-based rough membership C-means clustering

Abstract

Hard C-means (HCM) is one of the most widely used partitive clustering methods and was extended to rough C-means (RCM) by referencing to the perspective of rough set theory to deal with the certain, possible, and uncertain belonging of object to clusters. Furthermore, rough set C-means (RSCM) and rough membership C-means (RMCM) have been proposed as clustering models on an approximation space considering the granularity of the universe (object space) based on binary relations. Although these rough set-based C-means methods are practical, they are not formulated based on objective functions, but are built on heuristic schemes. Objective function-based methods can be a basis for discussion of the validity of clustering and further theoretical developments. In this paper, we propose a novel RMCM framework, which is called RMCM version 2 (RMCM2), based on an objective function. The objective function is designed to derive the same updating rule for cluster centers as in RMCM. We demonstrate the characteristics of RMCM2 by visualizing cluster boundaries on a grid point dataset. Furthermore, we verify the clustering performance of RMCM2 through numerical experiments by using real-world datasets.