# Clustering by Hill-Climbing: Consistency Results

arXiv: https://arxiv.org/abs/2202.09023 · HTML: https://mlsanity.com/paper/2202.09023/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [A Population Background for Nonparametric Density-Based Clustering](https://mlsanity.com/paper/1408.1381/) (2014)
- [Quickshift++: Provably Good Initializations for Sample-Based Mean Shift](https://mlsanity.com/paper/1805.07909/) (2018)
- [Density Level Sets: Asymptotics, Inference, and Visualization](https://mlsanity.com/paper/1504.05438/) (2015)
- [MeanShift++: Extremely Fast Mode-Seeking With Applications to Segmentation and Object Tracking](https://mlsanity.com/paper/2104.00303/) (2021)
- [On the Consistency of Quick Shift](https://mlsanity.com/paper/1710.10646/) (2017)
- [Nonparametric Inference For Density Modes](https://mlsanity.com/paper/1312.7567/) (2013)
- [Statistical Inference using the Morse-Smale Complex](https://mlsanity.com/paper/1506.08826/) (2015)
- [Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm](https://mlsanity.com/paper/2104.10103/) (2021)
- [An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree](https://mlsanity.com/paper/2111.10298/) (2021)

## Built on by (most cited first, 2 of 2)

- [Graph Max Shift: A Hill-Climbing Method for Graph Clustering](https://mlsanity.com/paper/2411.18794/) (2024)
- [Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift](https://mlsanity.com/paper/2608.05112/) (2026)

## Abstract (arXiv)

We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.