Objective function-based rough membership C-means clustering

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. (c) 2020 The Author(s). Published by Elsevier Inc.

Automated summary

Hard C-means (HCM) has been extended to rough C-means (RCM) to handle the certain, possible, and uncertain belonging of objects to clusters. Furthermore, rough set C-means (RSCM) and rough membership C-means (RMCM) have been proposed as clustering models based on binary relations in an approximation space. A novel RMCM framework, RMCM version 2 (RMCM2), has been proposed in this paper, which is based on an objective function and demonstrates characteristics through visualizing cluster boundaries and verifying clustering performance with real-world datasets.