Clustering based on local density peaks and graph cut

Abstract

Clustering by fast search and find of density peaks (DPC) is a widely used and studied clustering algorithm. In this article, we notice that DPC can achieve highly accurate clustering results when restricted to local neighborhoods. Therefore, by investigating density information in local neighborhoods, we propose to capture latent structures in data with family trees, which can reflect density dominations among nearest neighbors of data. A data set will then be partitioned into multiple family trees. In order to obtain the final clustering result, instead of exploiting the error-prone allocation strategy of DPC, we first elaborately design a novel similarity measure for family trees, characterizing not only the distance between data points, but also the structure of trees. Then, we adapt graph cut for the corresponding connection graph to also take global structural information into account. Extensive experiments on both real-world and synthetic data sets show that the proposed algorithm can outperform several prominent clustering algorithms for most of the cases, including the DPC and spectral clustering algorithms and some of their latest variants. We also analyze the robustness of the proposed algorithm w.r.t. hyper-parameters and its time complexity, as well as the necessity of its components through ablation study.