A Robust Automatic Merging Possibilistic Clustering Method

Krishnapuram and Keller [IEEE Trans. Fuzzy Syst., vol. 1, no. 2, pp. 98-110, May 1993] proposed a possibilistic
c
-means (PCM) clustering by relaxing the constraint in fuzzy
c
-means (FCMs) that the memberships of a data point across classes sum to 1. The PCM algorithm has a tendency to produce coincident clusters. This can be a merit of PCM as a good mode-seeking algorithm if initials and parameters are suitably chosen. However, the performance of PCM heavily depends on initializations and parameter selection. In this paper, we propose a mechanism of robust automatic merging. We then create an automatic merging possibilistic clustering method (AM-PCM), where the proposed algorithm does not only solve these parameter-selection and initialization problems but also obtains an optimal cluster number. The proposed AM-PCM algorithm first uses all data points as initial cluster centers and then automatically merges these surrounding points around each cluster mode such that it can self-organize data groups according to the original data structure. The AM-PCM can exhibit the robustness to parameter, noise, cluster number, different volumes, and initializations. The computational complexity of AM-PCM is also analyzed. Comparisons between AM-PCM and other clustering methods are made. Some numerical data and real datasets are used to show these good aspects of AM-PCM. Experimental results and comparisons actually demonstrate that the proposed AM-PCM is an effective and parameter-free robust clustering algorithm.