# Optimal Transport for Efficient, Unsupervised Anomaly Detection on Industrial Data

arXiv: https://arxiv.org/abs/2609.13940 · HTML: https://mlsanity.com/paper/2609.13940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 11 of 11)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [An Evaluation of the Human-Interpretability of Explanation](https://mlsanity.com/paper/1902.00006/) (2019)
- [A Survey on Explainable Anomaly Detection](https://mlsanity.com/paper/2210.06959/) (2022)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [Explainable Legal Case Matching via Inverse Optimal Transport-based Rationale Extraction](https://mlsanity.com/paper/2207.04182/) (2022)
- [Wasserstein-based fairness interpretability framework for machine learning models](https://mlsanity.com/paper/2011.03156/) (2020)
- [Conformalized density- and distance-based anomaly detection in time-series data](https://mlsanity.com/paper/1608.04585/) (2016)
- [Overcoming Representation Bias in Fairness-Aware data Repair using Optimal Transport](https://mlsanity.com/paper/2410.02840/) (2024)

## Abstract (arXiv)

Effective anomaly detection frameworks are a central pillar of the Industry 4.0 paradigm. In this paper, we introduce an Optimal Transport (OT)-based framework for anomaly detection, designed to detect deviations from normal behaviour in time-series sensor data. The OT-based method requires minimal user input and adapts to real-time data without the need for labelled training data. Our method effectively addresses existing limitations related to data labelling, generalisability, and scalability, demonstrating resilience against short-term fluctuations, noise, and data gaps - common challenges in industrial environments. Additionally, our method provides counterfactual explanations improving the auditability of the approach when deployed in industrial settings. The proposed method learns the mapping between normal and observed operating conditions through a sliding reference window that adapts to the dynamicity of the data. We evaluate our approach on three industrial datasets, from shipping, industrial HVAC systems, and publicly available benchmark data. The method was highly effective in identifying anomalies and reducing false positives, outperforming traditional methods, while maintaining computational efficiency and ease of configuration.