Single-Valued Neutrosophic Clustering Algorithm Based on Tsallis Entropy Maximization

• Published in: Axioms Vol. 7; no. 3; p. 57
• Main Authors: Li, Qiaoyan, Ma, Yingcang, Smarandache, Florentin, Zhu, Shuangwu
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2018
• Subjects: Algorithms; Clustering; Data compression; Decision support systems; Entropy; fuzzy c-means; Fuzzy sets; Image processing; Image segmentation; Lagrange multiplier; Machine learning; Methods; Optimization; Pattern recognition; picture fuzzy clustering; Similarity measures; single-valued neutrosophic set; Tsallis entropy; United States > US; China
• DOI: 10.3390/axioms7030057
• ISSN: 2075-1680

Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. The neutrosophic set, which is an extension of the fuzzy set, has received extensive attention in solving many real-life problems of inaccuracy, incompleteness, inconsistency and uncertainty. In this paper, we propose a new clustering algorithm, the single-valued neutrosophic clustering algorithm, which is inspired by fuzzy c-means, picture fuzzy clustering and the single-valued neutrosophic set. A novel suitable objective function, which is depicted as a constrained minimization problem based on a single-valued neutrosophic set, is built, and the Lagrange multiplier method is used to solve the objective function. We do several experiments with some benchmark datasets, and we also apply the method to image segmentation using the Lena image. The experimental results show that the given algorithm can be considered as a promising tool for data clustering and image processing.