Resolution-Aware Structural Density Peak Clustering

Density Peak Clustering (DPC) focuses on identifying centers and propagates labels at the sample level, which makes density estimation cutoff-sensitive and assignment chain-vulnerable, yielding suboptimal performance under heterogeneous densities and complex cluster structures. This paper argues that density peaks inference should instead be performed on resolution-controlled structural units: density becomes a stable count statistic, relative distance inherits the separation of the enclosing hierarchy, and assignment runs over a compact graph of structural units rather than long sample-to-sample chains. This view is realized in Resolution-Aware Structural Density Peak Clustering (RSDP), which builds a constrained hierarchy, selects an admissible level via a single resolution parameter, and applies a one-pass DPC rule on the selected structural units. Under a faithful-realization condition, it is proved that RSDP's empirical $\gamma$-ranking recovers the dominant population units and that its one-pass assignment recovers the sampled ground-truth partition. On synthetic and real-world datasets, RSDP achieves the highest ACC and NMI against state-of-the-art DPC variants, exceeding the strongest by 19.91% and 9.09% in average ACC and NMI, respectively.