# The EM Perspective of Directional Mean Shift Algorithm

arXiv: https://arxiv.org/abs/2101.10058 · HTML: https://mlsanity.com/paper/2101.10058/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [A review of mean-shift algorithms for clustering](https://mlsanity.com/paper/1503.00687/) (2015)
- [The modal age of Statistics](https://mlsanity.com/paper/1807.02789/) (2018)
- [On the Convergence of the Mean Shift Algorithm in the One-Dimensional Space](https://mlsanity.com/paper/1407.2961/) (2014)
- [Nonparametric Inference For Density Modes](https://mlsanity.com/paper/1312.7567/) (2013)
- [Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional Data](https://mlsanity.com/paper/2010.13523/) (2020)
- [Exact risk improvement of bandwidth selectors for kernel density estimation with directional data](https://mlsanity.com/paper/1306.0517/) (2013)
- [Nonparametric estimation of directional highest density regions](https://mlsanity.com/paper/2009.08915/) (2020)
- [Nonparametric multimodal regression for circular data](https://mlsanity.com/paper/2012.09915/) (2020)

## Built on by (most cited first, 1 of 1)

- [Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach](https://mlsanity.com/paper/2110.08505/) (2021)

## Abstract (arXiv)

The directional mean shift (DMS) algorithm is a nonparametric method for pursuing local modes of densities defined by kernel density estimators on the unit hypersphere. In this paper, we show that any DMS iteration can be viewed as a generalized Expectation-Maximization (EM) algorithm; in particular, when the von Mises kernel is applied, it becomes an exact EM algorithm. Under the (generalized) EM framework, we provide a new proof for the ascending property of density estimates and demonstrate the global convergence of directional mean shift sequences. Finally, we give a new insight into the linear convergence of the DMS algorithm.