A three-way clustering method based on improved density peaks algorithm and boundary detection graph

Density Peaks Clustering (DPC) is a classic density-based clustering algorithm that has been successfully applied in various areas. However, it assigns samples based on their nearest neighbors with higher density which may lead to an error propagation problem. Besides, it can not detect fringe and overlapping samples. To handle these defects, we improve the density measurement of DPC to make it more adaptive to different shapes and varying densities. Furthermore, we extend DPC to three-way clustering which means a sample in the positive region certainly belongs to the cluster, a sample in the boundary region belongs to the cluster partially and a sample in the negative region certainly does not belong to the cluster. In this paper, we propose a three-way clustering method called TW-RDPC. It mainly consists of three steps: (1) Identify cluster centers and assign other samples based on relative Cauchy kernel density to get initial clusters. (2) Detect potential boundary samples through boundary detection graph. (3) Determine whether potential boundary samples belong to multiple clusters based on the subordinate relationship to their k nearest neighbors. In order to validate TW-RDPC, we compare it to 7 algorithms on 10 synthetic datasets and 8 real-world datasets. Experimental results indicate that TW-RDPC is competitive with the compared 7 algorithms.