NECM: Neutrosophic evidential c-means clustering algorithm

A new clustering algorithm, neutrosophic evidential c-means (NECM) is introduced based on the neutrosophic set (NS) and the evidence theory. The clustering analysis is formulated as a constrained minimization problem, whose solution depends on an objective function. In the objective function of NECM, two new types of rejection have been introduced using NS theory: the ambiguity rejection which concerns the patterns lying near the class boundaries, and the distance rejection dealing with patterns that are far away from all the classes. A belief function evidence theory is employed to make the final decision, and it is defined using the concept of Dezert–Smarandache theory of plausible and paradoxical reasoning, which is a natural extension of the classical Dempster–Shafer theory. A variety of experiments were conducted using synthetic and real data sets. The results are promising and compared favorably with the results from the evidential c-means algorithm on the same data sets. We also applied the proposed method into the image segmentation. The experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing.