# Outlier detection in multivariate functional data through a contaminated mixture model

arXiv: https://arxiv.org/abs/2106.07222 · HTML: https://mlsanity.com/paper/2106.07222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 60 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Anomaly Detection in Univariate Time-series: A Survey on the State-of-the-Art](https://mlsanity.com/paper/2004.00433/) (2020)
- [Functional Isolation Forest](https://mlsanity.com/paper/1904.04573/) (2019)
- [Parsimonious mixtures of multivariate contaminated normal distributions](https://mlsanity.com/paper/1305.4669/) (2013)
- [Directional Outlyingness for Multivariate Functional Data](https://mlsanity.com/paper/1612.04615/) (2016)
- [Asymmetric Clusters and Outliers: Mixtures of Multivariate Contaminated Shifted Asymmetric Laplace Distributions](https://mlsanity.com/paper/1402.6744/) (2014)
- [A new look at the inverse Gaussian distribution](https://mlsanity.com/paper/1707.04400/) (2017)
- [Multiple Scaled Contaminated Normal Distribution and Its Application in Clustering](https://mlsanity.com/paper/1810.08918/) (2018)

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

- [Cluster weighted models for functional data](https://mlsanity.com/paper/2503.05159/) (2025)
- [Cluster weighted models with multivariate skewed distributions for functional data](https://mlsanity.com/paper/2504.12683/) (2025)
- [funOCLUST: Clustering Functional Data with Outliers](https://mlsanity.com/paper/2508.00110/) (2025)

## Abstract (arXiv)

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outliers. Model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms the competitors. Its application on the real data which motivated this study allows to correctly detect abnormal behaviors.