Self-Tuning Possibilistic c-Means Clustering Models

The relaxation of the probabilistic constraint of the fuzzy c-means clustering model was proposed to provide robust algorithms that are insensitive to strong noise and outlier data. These goals were achieved by the possibilistic c-means (PCM) algorithm, but these advantages came together with a sensitivity to cluster prototype initialization. According to the original recommendations, the probabilistic fuzzy c-means (FCM) algorithm should be applied to establish the cluster initialization and possibilistic penalty terms for PCM. However, when FCM fails to provide valid cluster prototypes due to the presence of noise, PCM has no chance to recover and produce a fine partition. This paper proposes a two-stage c-means clustering algorithm to tackle with most problems enumerated above. In the first stage called initialization, FCM with two modifications is performed: (1) extra cluster added for noisy data; (2) extra variable and constraint added to handle clusters of various diameters. In the second stage, a modified PCM algorithm is carried out, which also contains the cluster width tuning mechanism based on which it adaptively updates the possibilistic penalty terms. The proposed algorithm has less parameters than PCM when the number of clusters is $c>2$. Numerical evaluation involving synthetic and standard test data sets proved the advantages of the proposed clustering model.