Defuzzified clustering algorithms derived from the method of entropy-based fuzzy c-means

A class of hard c-means algorithms is derived from ´defuzzifying´ objective functions of the entropy-based fuzzy c-means and the KL-information based fuzzy c-means. Namely an entropy term is deleted from the objective functions while other parameters of cluster sizes and covariances are preserved. As a result, the objective function becomes linear with respect to the membership whereby a hard c-means algorithm is derived. Variations of the basic hard c-means algorithms are moreover proposed and reduction of computation using iterative matrix inversion is considered. Numerical examples are shown to compare results of proposed algorithms. Finally, a cluster validity measure is used whereby stability of clusters by different algorithms is compared.