# Gradient-Guided Density Peak Clustering

arXiv: https://arxiv.org/abs/2610.01050 · HTML: https://mlsanity.com/paper/2610.01050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 76 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 1 of 1)

- [A review of mean-shift algorithms for clustering](https://mlsanity.com/paper/1503.00687/) (2015)

## Abstract (arXiv)

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 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.