Cutset-type possibilistic c-means clustering algorithm

Abstract The possibilistic c-means (PCM) clustering algorithm was introduced to avoid the sensitivity of the fuzzy c-means (FCM) clustering algorithm to outliers by relaxing the column sum constraint of the membership matrix of the FCM, namely the between-class relationships. The membership value is then interpreted as the typicality value of a data point in the PCM which reflects the absolute distance of data point to one cluster well. However, the PCM has a significant defect of coincident clustering problem because of relaxing the relations of clusters. In this paper, a novel cutset-type possibilistic clustering (C-PCM) algorithm is proposed. The C-PCM firstly generates a cluster core resulting from a β-cutset for each cluster and searches for data points located inside the cluster core. Then, the typicalities of these points to other clusters are modified, thus introducing the between-class relationships and avoiding coincident clusters. Simultaneously an adaptive determination method is also given for the parameter β in the C-PCM. Moreover, a novel segmentation method for images corrupted by salt-and-pepper noise is proposed by taking advantage of the strong robustness of the C-PCM to outliers. Several experiments are done on synthetic data-sets, high dimensional data sets, noisy images, which demonstrate the good performance of the proposed algorithm.