# Analysis of a Generalized Expectation-Maximization Algorithm for Gaussian Mixture Models: A Control Systems Perspective

arXiv: https://arxiv.org/abs/1903.00979 · HTML: https://mlsanity.com/paper/1903.00979/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [Bridging Associative Memory and Probabilistic Modeling](https://mlsanity.com/paper/2402.10202/) (2024)
- [Clustering acoustic emission data streams with sequentially appearing clusters using mixture models](https://mlsanity.com/paper/2108.11211/) (2021)

## Abstract (arXiv)

The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM) algorithm in the context of Gaussian mixture models, where the maximization step in the EM is replaced by an increasing step. We show that this GEM algorithm can be understood as a linear time-invariant (LTI) system with a feedback nonlinearity. Therefore, we explore some of its convergence properties by leveraging tools from robust control theory. Lastly, we explain how the proposed GEM can be designed, and present a pedagogical example to understand the advantages of the proposed approach.