NCM: Neutrosophic c-means clustering algorithm

In this paper, a new clustering algorithm, neutrosophic c-means (NCM), is introduced for uncertain data clustering, which is inspired from fuzzy c-means and the neutrosophic set framework. To derive such a structure, a novel suitable objective function is defined and minimized, and the clustering problem is formulated as a constrained minimization problem, whose solution depends on the objective function. In the objective function, two new types of rejection have been introduced: the ambiguity rejection which concerns the patterns lying near the cluster boundaries, and the distance rejection dealing with patterns that are far away from all the clusters. These measures are able to manage uncertainty due to imprecise and/or incomplete definition of the clusters. We conducted several experiments with synthetic and real data sets. The results are encouraging and compared favorably with results from other methods as FCM, PCM and FPCM algorithms on the same data sets. Finally, the proposed method was applied into image segmentation algorithm. The experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing.