KNCM: Kernel Neutrosophic c-Means Clustering

• Published in: Applied soft computing Vol. 52; pp. 714 - 724
• Main Authors: Akbulut, Yaman, Şengür, Abdulkadir, Guo, Yanhui, Polat, Kemal
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-03-2017
• Subjects: Data clustering; Fuzzy clustering; Kernel function; Neutrosophic c-means; Neutrosophic c-means; Kernel function; Fuzzy clustering; Data clustering
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2016.10.001

The block diagram of the proposed Kernel-NCM approach.
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•We proposed a new Kernel Neutrosophic c- Means (KNCM) algorithm for improving the NCM method on the nonlinearly separable datasets.•In addition, new membership and prototype update equations were derived from minimization of the proposed cost function.•The developed KNCM method was applied on variety of applications such as toy dataset clustering, real dataset clustering and noisy image segmentation. The obtained results were compared with the KFCM method. The obtained results showed that the proposed KNCM method yielded better results than KFCM.
Data clustering is an important step in data mining and machine learning. It is especially crucial to analyze the data structures for further procedures. Recently a new clustering algorithm known as ‘neutrosophic c-means’ (NCM) was proposed in order to alleviate the limitations of the popular fuzzy c-means (FCM) clustering algorithm by introducing a new objective function which contains two types of rejection. The ambiguity rejection which concerned patterns lying near the cluster boundaries, and the distance rejection was dealing with patterns that are far away from the clusters. In this paper, we extend the idea of NCM for nonlinear-shaped data clustering by incorporating the kernel function into NCM. The new clustering algorithm is called Kernel Neutrosophic c-Means (KNCM), and has been evaluated through extensive experiments. Nonlinear-shaped toy datasets, real datasets and images were used in the experiments for demonstrating the efficiency of the proposed method. A comparison between Kernel FCM (KFCM) and KNCM was also accomplished in order to visualize the performance of both methods. According to the obtained results, the proposed KNCM produced better results than KFCM.