Clustering by connection center evolution

TL;DR

This paper introduces a novel clustering method based on the evolution of connection centers across scales, utilizing powers of a similarity matrix to dynamically identify meaningful clusters without predefining their number.

Contribution

The study proposes a new scale-adaptive clustering approach using connection centers and matrix powers, enabling automatic determination of appropriate cluster numbers and scales.

Findings

Cluster centers evolve from local to global with increasing matrix power.

The method can automatically skip unreasonable cluster numbers.

It effectively suggests suitable observation scales for data analysis.

Abstract

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