# On the Convergence of the Mean Shift Algorithm in the One-Dimensional Space

arXiv: https://arxiv.org/abs/1407.2961 · HTML: https://mlsanity.com/paper/1407.2961/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2014.

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

- [Weighted quantization using MMD: From mean field to mean shift via gradient flows](https://mlsanity.com/paper/2502.10600/) (2025)
- [MeanShift++: Extremely Fast Mode-Seeking With Applications to Segmentation and Object Tracking](https://mlsanity.com/paper/2104.00303/) (2021)
- [Convergence Analysis of Mean Shift](https://mlsanity.com/paper/2305.08463/) (2023)
- [The EM Perspective of Directional Mean Shift Algorithm](https://mlsanity.com/paper/2101.10058/) (2021)
- [Variational Auto Encoder Gradient Clustering](https://mlsanity.com/paper/2105.06246/) (2021)
- [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 algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine vision, pattern recognition, and image processing. Although the mean shift algorithm has been used in many applications, a rigorous proof of its convergence is still missing in the literature. In this paper we address the convergence of the mean shift algorithm in the one-dimensional space and prove that the sequence generated by the mean shift algorithm is a monotone and convergent sequence.