Density peaks clustering based on local fair density and fuzzy k-nearest neighbors membership allocation strategy

Abstract

The density peaks clustering algorithm (DPC) has been widely concerned since it was proposed in 2014. There is no need to specify in advance and only one parameter required. However, some disadvantages are still witnessed in DPC: (1) Requiring repeated experiments for choosing a suitable calculation method of the local density due to the variations in the scale of the dataset, which will lead to additional time cost. (2) Difficulty in finding an optimal cutoff distance threshold, since different parameters not only impact the selection of cluster centers but also directly affect the quality of clusters. (3) Poor fault tolerance of the allocation strategy, especially in manifold datasets or datasets with uneven density distribution. Targetting solutions to these problems, a density peaks clustering based on local fair density and fuzzy k-nearest neighbors membership allocation strategy (LF-DPC) is proposed in this paper. First, to obtain a more balanced local density, two classic local density calculation methods are combined in the algorithm to calculate the local fair density through the optimization function with the smallest local density difference. Second, a robust two stage remaining points allocation strategy is designed. In the first stage, k-nearest neighbors are used to quickly and accurately allocate points from the cluster center. In the second stage, to further improve the accuracy of allocation, a fuzzy k-nearest neighbors membership method is designed to allocate the remaining points. Finally, the LF-DPC algorithm has been experimented based on several synthetic and real-world datasets. The results prove that the proposed algorithm has obvious advantages compared with the other five ones.