Clustering by connection center evolution

The determination of clustering centers generally depends on the observation scale that we use to analyze the data to be clustered. An inappropriate scale usually leads to unreasonable clustering centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of vertices in an undirected graph, then present the concept of connection center and regard it as the clustering center of the data. Based on this definition, the determination of clustering centers and the assignment of class become very simple, natural and effective. One more crucial finding is that the clustering centers of different scales can be obtained easily by different powers of a similarity matrix, and the change of power from small to large leads to the dynamic evolution of clustering centers from local (microscopic) to global (macroscopic). Further, in this process of evolution, the number of clusters changes discontinuously, which means that the presented method can automatically skip the unreasonable number of clusters, suggest appropriate observation scales and provide corresponding clustering results. (C) 2019 Elsevier Ltd. All rights reserved.