# Asymmetric Clusters and Outliers: Mixtures of Multivariate Contaminated Shifted Asymmetric Laplace Distributions

arXiv: https://arxiv.org/abs/1402.6744 · HTML: https://mlsanity.com/paper/1402.6744/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2014.

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

- [Outlier detection in multivariate functional data through a contaminated mixture model](https://mlsanity.com/paper/2106.07222/) (2021)
- [Clustering Three-Way Data with Outliers](https://mlsanity.com/paper/2310.05288/) (2023)
- [Heckman Selection Contaminated Normal Model](https://mlsanity.com/paper/2409.12348/) (2024)

## Abstract (arXiv)

Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related non-contaminated mixture, for each (asymmetric) cluster, our model has one parameter controlling the proportion of outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach that is absent from other approaches such as trimming. Moreover, each observation is given a posterior probability of belonging to a particular cluster, and of being an outlier or not; advantageously, this allows for the automatic detection of outliers. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. The behaviour of the proposed model is investigated, and compared with well-established finite mixtures, on artificial and real data.