# Abnormal component analysis

arXiv: https://arxiv.org/abs/2312.16139 · HTML: https://mlsanity.com/paper/2312.16139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 26 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Anomaly Detection by Robust Statistics](https://mlsanity.com/paper/1707.09752/) (2017)
- [A Framework to Learn with Interpretation](https://mlsanity.com/paper/2010.09345/) (2020)
- [Choosing among notions of multivariate depth statistics](https://mlsanity.com/paper/2004.01927/) (2020)
- [Detecting deviating data cells](https://mlsanity.com/paper/1601.07251/) (2016)
- [Anomaly detection using data depth: multivariate case](https://mlsanity.com/paper/2210.02851/) (2022)
- [Confidence regions and minimax rates in outlier-robust estimation on the probability simplex](https://mlsanity.com/paper/1902.04650/) (2019)

## Abstract (arXiv)

At the crossway of machine learning and data analysis, anomaly detection 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 and isolation constitute an important task in almost any area of industry and science. While a substantial body of literature is devoted to detection of anomalies, little attention is payed to their explanation. This is the case mostly due to intrinsically non-supervised nature of the task and non-robustness of the exploratory methods like principal component analysis (PCA). We introduce a new statistical tool dedicated for exploratory analysis of abnormal observations using data depth as a score. Abnormal component analysis (shortly ACA) is a method that searches a low-dimensional data representation that best visualises and explains anomalies. This low-dimensional representation not only allows to distinguish groups of anomalies better than the methods of the state of the art, but as well provides a -- linear in variables and thus easily interpretable -- explanation for anomalies. In a comparative simulation and real-data study, ACA also proves advantageous for anomaly analysis with respect to methods present in the literature.