Research on Generalized Fuzzy C-Means Clustering Algorithm with Improved Fuzzy Partitions

Cluster analysis is an important tool of unsupervised pattern recognition. It has been used in diverse fields such as data mining, biology, computer vision, and document analysis. The fuzziness index m has important influence on the clustering result of fuzzy clustering algorithms and it should not be forced to fix at the usual value m=2. In view of its distinctive features in applications and its limitation of having m=2 only, a recent advance of fuzzy clustering called fuzzy c-means clustering with improved fuzzy partitions (IFP-FCM) is extended in this paper and a generalized algorithm called GIFP-FCM for more effective clustering is proposed. By introducing a novel membership constraint function, a new objective function is constructed and GIFP-FCM clustering is derived. Meanwhile, from the viewpoints of Voronoi distance and competitive learning, the robustness and convergence of the proposed algorithm are analyzed. The proposed GIFP-FCM algorithm not only inherits the merits of IFP-FCM, but also generalizes it so that the original limitation on the fuzziness index m can be removed. Furthermore, the classical fuzzy c-means algorithm (FCM) and IFP-FCM can be taken as two special cases of the proposed algorithm, and GIFP-FCM provides a reasonable link between FCM and IFP-FCM. Several experimental results including its application to noisy image texture segmentation demonstrate its average advantage over FCM and IFP-FCM in both clustering and robustness capability.