Gradient-Guided Density Peak Clustering
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.
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BibTeX
@misc{zhang2026gradientguided,
title = {{Gradient-Guided Density Peak Clustering}},
author = {Yikun Zhang and Yen-Chi Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01050},
eprint = {2610.01050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01050},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gradient-Guided Density Peak Clustering
AU - Yikun Zhang
AU - Yen-Chi Chen
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01050
UR - https://arxiv.org/abs/2610.01050
AB - 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.
ER -