Fast kernel fuzzy c-means algorithms based on difference of convex programming

In this study, we propose three new algorithms based on difference of convex (DC) programming and DC algorithm (DCA) for kernel fuzzy c-means (KFCM) clustering model. Firstly, KFCM model is reformulated into two equivalent forms of DC programmings for which different KFCM algorithms are designed. Then, to further accelerate the second DCA based KFCM algorithm, we adopt an approximate strategy which is demonstrated effectiveness by experiments, as it constructs cluster centers to be linear combinations of a few randomly selected samples instead of full of them. In order to find a good initial point, we develop an alternative procedure of KFCM and our proposed DCA based KFCM algorithms. The proposed DCA based KFCM algorithms are efficient because they only require to compute the projection of points onto a sphere at each iteration, which is inexpensive. Numerical results on several real world datasets show that the proposed algorithms based on DCA for KFCM model is more efficient than classical KFCM algorithm with regard to accuracies, running-time and iterative times.