# Convergence Analysis of Mean Shift

arXiv: https://arxiv.org/abs/2305.08463 · HTML: https://mlsanity.com/paper/2305.08463/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 68 references that are in the map.
- First posted on arXiv 15 May 2023.

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

- [Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods](https://mlsanity.com/paper/1602.02915/) (2016)
- [Splitting methods with variable metric for KL functions](https://mlsanity.com/paper/1405.1357/) (2014)
- [Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs](https://mlsanity.com/paper/1409.8147/) (2014)
- [Nonparametric modal regression](https://mlsanity.com/paper/1412.1716/) (2014)
- [Mixture model modal clustering](https://mlsanity.com/paper/1609.04721/) (2016)
- [Maximum Number of Modes of Gaussian Mixtures](https://mlsanity.com/paper/1702.05066/) (2017)
- [On the Convergence of the Mean Shift Algorithm in the One-Dimensional Space](https://mlsanity.com/paper/1407.2961/) (2014)
- [On Convergence of Epanechnikov Mean Shift](https://mlsanity.com/paper/1711.07441/) (2017)
- [Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm](https://mlsanity.com/paper/2001.11168/) (2020)
- [Optimal Kernel for Kernel-Based Modal Statistical Methods](https://mlsanity.com/paper/2304.10046/) (2023)

## Built on by (most cited first, 6 of 6)

- [Contrastive Mean-Shift Learning for Generalized Category Discovery](https://mlsanity.com/paper/2404.09451/) (2024)
- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [Sketch and shift: a robust decoder for compressive clustering](https://mlsanity.com/paper/2312.09940/) (2023)
- [Unleashing the Potential of All Test Samples: Mean-Shift Guided Test-Time Adaptation](https://mlsanity.com/paper/2507.00462/) (2025)
- [Local Averaging Accurately Distills Manifold Structure From Noisy Data](https://mlsanity.com/paper/2506.18761/) (2025)
- [Convergence and clustering analysis for Mean Shift with radially symmetric, positive definite kernels](https://mlsanity.com/paper/2506.19837/) (2025)

## Abstract (arXiv)

The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly mild conditions, with the help of the argument concerning the Lojasiewicz inequality. Our findings extend existing ones covering analytic kernels and the Epanechnikov kernel. Those are significant in that they cover the biweight kernel, which is optimal among non-negative kernels in terms of the asymptotic statistical efficiency for the KDE-based mode estimation.