A generalized fuzzy-possibilistic c-means clustering algorithm

The so-called fuzzy-possibilistic c-means (FPCM) algorithm was introduced as an early mixed-partition method aiming to eliminate some adverse effects present in the behavior of the fuzzy c-means (FCM) and the possibilistic c-means (PCM) algorithms. A great advantage of FPCM was the low number of its parameters, as it eliminated the possibilistic penalty terms used by PCM. Unfortunately, FPCM in its original formulation also has a weak point: the strength of the possibilistic term is in inverse proportion with the number of clustered data items, which makes FPCM act like FCM when clustering large sets of data. This paper proposes a modification of the FPCM algorithm by introducing an extra coefficient into the possibilistic term that allows us to control the strength of the possibilistic effect within the mixture model. The modified clustering model will be referred to as generalized FPCM, since a certain value of the extra parameter reduces it to the original FPCM, or in other words, FPCM is a special case of the proposed algorithm. The proposed method is evaluated using noise-free and noisy data as well.