An improved possibilistic C-Means algorithm with finite rejection and robust scale estimation

We propose an improved Possibilistic C-Means (PCM) algorithm called the New Possibilistic C-Means algorithm (NPCM). The NPCM solves the problems associated with the traditional PCM, namely the extreme dependence on a good initialization and an accurate estimate of scale. The connection between the PCM and M-, and W-estimators is exploited to robustify the PCM memberships by forcing finite rejection of the outliers and by integrating a dynamic and robust scale estimation scheme in the alternative optimization process of the PCM objective function. We further extend the algorithm to the case of multivariate Gaussian clusters where we propose a new 50% breakdown scheme to estimate the covariance matrices. The initialization scheme is also refined to yield better prototype estimates. The resulting algorithm is proved to be superior in performance to the hard, fuzzy, and original possibilistic clustering algorithms.