# Convergence Analysis of Blurring Mean Shift

arXiv: https://arxiv.org/abs/2402.15146 · HTML: https://mlsanity.com/paper/2402.15146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 51 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 7 of 7)

- [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)
- [Mixture model modal clustering](https://mlsanity.com/paper/1609.04721/) (2016)
- [On Convergence of Epanechnikov Mean Shift](https://mlsanity.com/paper/1711.07441/) (2017)
- [On the Convergence and Consistency of the Blurring Mean-Shift Process](https://mlsanity.com/paper/1305.1040/) (2013)
- [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, 1 of 1)

- [Doubly Stochastic Mean-Shift Clustering](https://mlsanity.com/paper/2602.15393/) (2026)

## Abstract (arXiv)

Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper, we analyze convergence properties of the BMS algorithm by leveraging its interpretation as an optimization procedure, which is known but has been underutilized in existing convergence studies. Whereas existing results on convergence properties applicable to multi-dimensional data only cover the case where all the blurred data point sequences converge to a single point, this study provides a convergence guarantee even when those sequences can converge to multiple points, yielding multiple clusters. This study also shows that the convergence of the BMS algorithm is fast by further leveraging geometrical characterization of the convergent points.