A Comparison between K-Means, FCM and ckMeans Algorithms

Fuzzy C-Means, introduced by Jim Bezdek in 1981 is one of the earliest and most popular fuzzy clustering algorithms. However, in order to improve the hit rate or speed, over the years several modifications have been proposed. Among these we highlight the ckMeans algorithm proposed by us in 2010 which make a change in the way to calculate the center of the clusters of FCM. The idea is to use an auxiliary membership function of elements to those clusters that are essentially crisp and calculate the centroids following a similar process as done in K-Means algorithm but keeping the same procedures as in FCM in the rest of algorithm. In fact, this hybridization between FCM and K-Means motivated the name ckMeans for this variant of the FCM. In this article we apply K-Means, FCM and ckMeans algorithms in a validated database of mammograms with about a thousand elements and compare these three algorithms in terms of hit rate and number of each iterations and the computational processing time until the convergency of the system.