# Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport

arXiv: https://arxiv.org/abs/2502.12793 · HTML: https://mlsanity.com/paper/2502.12793/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Efficient GAN-Based Anomaly Detection](https://mlsanity.com/paper/1802.06222/) (2018)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [Anomaly Detection in Trajectory Data with Normalizing Flows](https://mlsanity.com/paper/2004.05958/) (2020)
- [Optimal Transportation Theory with Repulsive Costs](https://mlsanity.com/paper/1506.04565/) (2015)
- [Benchmarking Domain Adaptation for Chemical Processes on the Tennessee Eastman Process](https://mlsanity.com/paper/2308.11247/) (2023)

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

- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Multi-Domain Clustering via Measure Quantization](https://mlsanity.com/paper/2609.21664/) (2026)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Detecting anomalies in datasets is a longstanding problem in machine learning. In this context, anomalies are defined as a sample that significantly deviates from the remaining data. Meanwhile, optimal transport (OT) is a field of mathematics concerned with the transportation, between two probability measures, at least effort. In classical OT, the optimal transportation strategy of a measure to itself is the identity. In this paper, we tackle anomaly detection by forcing samples to displace its mass, while keeping the least effort objective. We call this new transportation problem Mass Repulsing Optimal Transport (MROT). Naturally, samples lying in low density regions of space will be forced to displace mass very far, incurring a higher transportation cost. We use these concepts to design a new anomaly score. Through a series of experiments in existing benchmarks, and fault detection problems, we show that our algorithm improves over existing methods.