AHDPC: Adaptively hyperbolic density peak clustering

Non-uniformly distributed datasets are common in real-world, and density peak clustering (DPC) methods are used on these datasets due to their superior clustering performance. However, existing DPC relies on linearly growing Euclidean distance, causing misleading similarity between points from different clusters and limiting the improvement of accuracy. To overcome this limitation, this study introduces an adaptive hyperbolic density peak clustering algorithm (AHDPC) by extending DPC into hyperbolic space. First, linear Euclidean distance is replaced with exponentially growing hyperbolic distance to enhance density difference between different points. Then, to overcome the misclassification of points at the junction of high-density and low-density regions and errors from extreme hyperbolic distance, a novel adaptive weighting strategy is proposed, it dynamically adjusts hyperbolic distance by building the trace of the global covariance matrix, the Euclidean norm, the maximum pairwise distance, and point-to-center deviation. Finally, an adaptively cutoff distance method based on a segmented search strategy is developed to eliminate manual tuning, and an exponential density function replaces the gaussian kernel to improve computational efficiency. AHDPC not only overcomes the deficiencies of Euclidean space but also mitigates the restrictive aspects of hyperbolic space. Extensive experiments on synthetic and real datasets, the olivetti faces dataset, and medical image datasets demonstrate that AHDPC outperforms state-of-the-art methods in clustering accuracy. Results also show that AHDPC produces more discriminative decision graph for identifying cluster centers and enhances the accuracy of categorisation of non-center points. The advantages of its robustness and adaptive weight in improving the clustering performance are also confirmed.