# Penalized Maximum Likelihood Estimator for Mixture of von Mises-Fisher Distributions

arXiv: https://arxiv.org/abs/2009.02921 · HTML: https://mlsanity.com/paper/2009.02921/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2020.

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

- [SeFEF: A Seizure Forecasting Evaluation Framework](https://mlsanity.com/paper/2510.11275/) (2025)

## Abstract (arXiv)

The von Mises-Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises-Fisher distributions have found numerous applications. However, the likelihood function for the finite mixture of von Mises-Fisher distributions is unbounded and consequently the maximum likelihood estimation is not well defined. To address the problem of likelihood degeneracy, we consider a penalized maximum likelihood approach whereby a penalty function is incorporated. We prove strong consistency of the resulting estimator. An Expectation-Maximization algorithm for the penalized likelihood function is developed and simulation studies are performed to examine its performance.