# Finding Outliers in Gaussian Model-Based Clustering

arXiv: https://arxiv.org/abs/1907.01136 · HTML: https://mlsanity.com/paper/1907.01136/

## Key facts

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

## Built on by (most cited first, 3 of 3)

- [Clustering Three-Way Data with Outliers](https://mlsanity.com/paper/2310.05288/) (2023)
- [funOCLUST: Clustering Functional Data with Outliers](https://mlsanity.com/paper/2508.00110/) (2025)
- [Wasserstein Filtering: A Sample Selection Method for Robust Distribution Learning](https://mlsanity.com/paper/2608.13418/) (2026)

## Abstract (arXiv)

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample squared Mahalanobis distance is beta-distributed is used to derive an approximate distribution for the log-likelihoods of subset finite Gaussian mixture models. An algorithm is then proposed that removes the least plausible points according to the subset log-likelihoods, which are deemed outliers, until the subset log-likelihoods adhere to the reference distribution. This results in a trimming method, called OCLUST, that inherently estimates the number of outliers.