Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport

Eduardo Fernandes Montesuma, EL HABAZI Adel, Fred Maurice NGOLE MBOULA

Abstract: 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 distribution, at least effort. In classical OT, the optimal transportation strategy of a distribution to itself is the identity, i.e., each sample keeps its mass. 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. In contrast, samples on high density regions are able to send their mass just outside an \emph{exclusion zone}. 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. Our code is publicly available at https://github.com/eddardd/MROT

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Bernhard_C_Geiger1

Submission Number: 4390