# Anomaly detection using data depth: multivariate case

arXiv: https://arxiv.org/abs/2210.02851 · HTML: https://mlsanity.com/paper/2210.02851/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 95 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks](https://mlsanity.com/paper/2112.05355/) (2021)
- [Choosing among notions of multivariate depth statistics](https://mlsanity.com/paper/2004.01927/) (2020)
- [Exact computation of the halfspace depth](https://mlsanity.com/paper/1411.6927/) (2014)
- [Depth for curve data and applications](https://mlsanity.com/paper/1901.00180/) (2019)
- [Lens depth function and k-relative neighborhood graph: versatile tools for ordinal data analysis](https://mlsanity.com/paper/1602.07194/) (2016)
- [Depth and depth-based classification with R-package ddalpha](https://mlsanity.com/paper/1608.04109/) (2016)
- [Depth-based Runs Tests for Bivariate Central Symmetry](https://mlsanity.com/paper/1401.2377/) (2014)
- [On Generalization and Computation of Tukey's Depth: Part I](https://mlsanity.com/paper/2112.08475/) (2021)
- [On Generalization and Computation of Tukey's Depth: Part II](https://mlsanity.com/paper/2112.08478/) (2021)

## Built on by (most cited first, 4 of 4)

- [Data Depth as a Risk](https://mlsanity.com/paper/2507.08518/) (2025)
- [Abnormal component analysis](https://mlsanity.com/paper/2312.16139/) (2023)
- [seMCD: Sequentially implemented Monte Carlo depth computation with statistical guarantees](https://mlsanity.com/paper/2507.06227/) (2025)
- [RareSense: Rarity-Aware Similarity Search for Anomaly Retrieval in Transactional Data](https://mlsanity.com/paper/2607.28879/) (2026)

## Abstract (arXiv)

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items) or failed equipment, financial frauds or crisis events, their on-time identification, isolation and explanation constitute an important task in almost any branch of science and industry. By providing a robust ordering, data depth - statistical function that measures belongingness of any point of the space to a data set - becomes a particularly useful tool for detection of anomalies. Already known for its theoretical properties, data depth has undergone substantial computational developments in the last decade and particularly recent years, which has made it applicable for contemporary-sized problems of data analysis and machine learning. In this article, data depth is studied as an efficient anomaly detection tool, assigning abnormality labels to observations with lower depth values, in a multivariate setting. Practical questions of necessity and reasonability of invariances and shape of the depth function, its robustness and computational complexity, choice of the threshold are discussed. Illustrations include use-cases that underline advantageous behaviour of data depth in various settings.