title: A Self-Adaptive Fuzzyc-Means Algorithm for Determining the Optimal Number of Clusters.
abstract: For the shortcoming of fuzzyc-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rule [Formula: see text] and obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result.
authors.affiliation: School of Information Science and Engineering, Shandong Normal University, Jinan, Shandong, China; School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong, China; Shandong Provincial Key Laboratory for Distributed Computer Software Novel Technology, Jinan, Shandong, China.
authors.forename: Min
authors.identifier: 0000-0002-6763-3297
authors.initials: M
authors.lastname: Ren
authors.affiliation: School of Information Science and Engineering, Shandong Normal University, Jinan, Shandong, China; Shandong Provincial Key Laboratory for Distributed Computer Software Novel Technology, Jinan, Shandong, China.
authors.forename: Peiyu
authors.identifier: 0000-0001-9450-3837
authors.initials: P
authors.lastname: Liu
authors.affiliation: School of Information Science and Engineering, Shandong Normal University, Jinan, Shandong, China; Shandong Provincial Key Laboratory for Distributed Computer Software Novel Technology, Jinan, Shandong, China.
authors.forename: Zhihao
authors.initials: Z
authors.lastname: Wang
authors.affiliation: School of Information Science and Engineering, Shandong Normal University, Jinan, Shandong, China; Shandong Provincial Key Laboratory for Distributed Computer Software Novel Technology, Jinan, Shandong, China.
authors.forename: Jing
authors.initials: J
authors.lastname: Yi
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D066264:Datasets as Topic; D017143:Fuzzy Logic; D006801:Humans; D010363:Pattern Recognition, Automated