Modified fuzzy clustering with segregated cluster centroids

Abstract

In this paper, we firstly propose a novel strategy to fuse k-means and fuzzy c-means objective functions from a multi-objective problem into a unified model, such that extreme difficulty of choosing the optimal level of the cluster fuzziness can be avoided (level of the cluster fuzziness vanishes). Accordingly, fused k-means and fuzzy c-means clustering (FKMFCM) problem is achieved with a brand new form. Based on the proposed FKMFCM, novel degrees of membership could be further derived with the closed forms. Additionally, a penalty problem is further introduced to the proposed FKMFCM, such that the fuzzy cluster centroids are modified to be more segregated from each other. Consequently, FKMFCM with the modified cluster centroid (FKMFCM-MCC) problem is represented as a bi-objective optimization for the efficient clustering. To address the proposed FKMFCM-MCC problem, an original characteristic function is introduced, such that the corresponding algorithm converges to the global optimum of the proposed FKMFCM-MCC problem. Eventually, theoretical analysis along with the empirical result is provided to validate the effectiveness of the proposed FKMFCM-MCC approach.