Graph-based density peak merging for identifying multi-peak clusters

Density peaks clustering (DPC), which is short for clustering by fast search-and-find of density peaks, is a recently developed density-based clustering method that is widely used because of its effective detection of isolated high-density regions. However, it often fails to identify true cluster structures from data owing to its intrinsic assumption that a cluster has a unique and high-density center, because a single cluster can contain several peaks. We call this the “multi-peak problem”. To overcome this, we propose a peak merging method for clustering. In the proposed algorithm, a valley and its local density are defined to identify the intersection between two adjoined peaks. These are used to construct directed and connected subgraphs, using which we merge multiple peaks if needed. Unlike DPC and its variants, the proposed method is capable of identifying highly complex shaped clusters with no interpretation of the decision graph. Numerical experiments based on synthetic and real datasets demonstrated that our method outperformed the benchmarking methods.