Adaptive density peak clustering based on Delaunay graph.

Clustering is a fundamental tool in data mining, widely used in various fields such as image segmentation, data science, pattern recognition, and bioinformatics. Density Peak Clustering (DPC) is a density-based method that identifies clusters by calculating the local density of data points and selecting cluster centers based on these densities. However, DPC has several limitations. First, it requires a cutoff distance to calculate local density, and this parameter varies across datasets, which requires manual tuning and affects the algorithm's performance. Second, the number of cluster centers must be manually specified, as the algorithm cannot automatically determine the optimal number of clusters, making the algorithm dependent on human intervention. To address these issues, we propose an adaptive Density Peak Clustering (DPC) method, which automatically adjusts parameters like cutoff distance and the number of clusters, based on the Delaunay graph. This approach uses the Delaunay graph to calculate the connectivity between data points and prunes the points based on these connections, automatically determining the number of cluster centers. Additionally, by optimizing clustering indices, the algorithm automatically adjusts its parameters, enabling clustering without any manual input. Experimental results on both synthetic and real-world datasets demonstrate that the proposed algorithm outperforms similar methods in terms of both efficiency and clustering accuracy.