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.
