Work

Gradient-Guided Density Peak Clustering

Year: 2026

Type: preprint

Abstract: Density peak clustering (DPC) connects each observation to its nearest neighbor of higher density and identifies cluster centers as high-density observations with unusually large nearest neighbor uphill shifts. The resulting uphill paths from observations to cluster centers, however, can be irregular and unstable in low-density regions, making the clustering assignments sensitive to local perturbations and obscuring the population geometry of the DPC graph. In this paper, we introduce \emph{gradient-guided density peak clustering} (GGDPC), which performs a gradient ascent step before each nearest neighbor uphill search. We develop a stability theory that relates the GGDPC graph to the gradient ascent flow of the population density. In particular, we establish consistency of GGDPC under five complementary criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. Together, these results provide new statistical, geometric, and topological interpretations of DPC-type clustering algorithms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01050

Authors: Zhang, Yikun, Chen, Yen-Chi

Institutions: University of Chicago, NSF-Simons AI Institute for the Sky, University of Washington

Language: English

Topic: Advanced Clustering Algorithms Research

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institutes of Health

Awards: Novel Missing Data Approaches for Corrupted Longitudinal Data, Data-Enabled Acceleration of Stochastic Computational Experiments, CAREER: Inference with graphs: density skeleton and Markov missing graph

OpenAlex ID: W7215951403

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