Three-way evidence theory-based density peak clustering with the principle of justifiable granularity

Clustering by fast search and find of density peaks (DPC) is an effective clustering approach that can find all the cluster centers at once with just one parameter and without iterative processing. However, the cutoff distance, a key parameter of density measurement in the DPC approach, affects the quality of the final clustering results. Its selection relies on experimental experience and lacks of a semantic explanation. Furthermore, the allocation strategy of the traditional DPC approach may cause several points to be assigned incorrectly, leading to subsequent points being assigned incorrectly and ultimately forming continuous allocation errors. To overcome the deficiencies, this paper proposes a novel three-way evidence theory-based density peak clustering with the principle of justifiable granularity (3 W-PEDP). First, the computation of the cutoff distance is converted into the search for nearest neighbors. From the perspective of granular computing, 3 W-PEDP transforms the neighbor selection issue into the construction of justifiable granularity. And the optimal neighbors can be achieved with the construction of coverage and specificity criteria. Second, inspired by three-way clustering, we adopt a twostage method for sample allocation. On the one hand, for core point allocation, a two-layer nearest neighbor is constructed based on the achieved optimal neighbors. On the other hand, we designed a new evidence mass function to guide us in assigning the remaining points. In this novel evidence mass function, not only the labels of the assigned samples are considered, but also the information of the neighborhoods around the unassigned samples is fused. Finally, we assess the effectiveness of 3 W-PEDP on numerous public synthetic datasets and UCI real-world datasets. Then, detail comparing results with several popular clustering methods are presented. In addition, experimental studies verify the effectiveness of constructing justifiable granularity in selecting the optimal neighbors. The experimental results demonstrate 3 W-PEDP has good adaptability and robustness, which can achieve better clustering performance. Our source code is available at https://github.com/Luyangabc/ 3W-PEDP.