Generalization rules for the suppressed fuzzy c-means clustering algorithm

Intending to achieve an algorithm characterized by the quick convergence of hard c-means (HCM) and finer partitions of fuzzy c-means (FCM), suppressed fuzzy c-means (s-FCM) clustering was designed to augment the gap between high and low values of the fuzzy membership functions. Suppression is produced via modifying the FCM iteration by creating a competition among clusters: for each input vector, lower degrees of membership are proportionally reduced, being multiplied by a previously set constant suppression rate, while the largest fuzzy membership grows to maintain the probabilistic constraint. Even though so far it was not treated as an optimal algorithm, it was employed in a series of applications, and reported to be accurate and efficient in various clustering problems. In this paper we introduce some generalized formulations of the suppression rule, leading to an infinite number of new clustering algorithms. Further on, we identify the close relation between s-FCM clustering models and the so-called FCM algorithm with generalized improved partition (GIFP-FCM). Finally we reveal the constraints under which the generalized s-FCM clustering models minimize the objective function of GIFP-FCM, allowing us to call our suppressed clustering models optimal. Based on a large amount of numerical tests performed in multidimensional environment, several generalized forms of suppression proved to give more accurate partitions than earlier solutions, needing significantly less iterations than the conventional FCM.