通过强制样本远离低密度区域，用最优传输成本检测异常点。
Unsupervised Anomaly Detection through Mass Repulsing Optimal Transport
- 设计新方法MROT，让样本在保持最小移动代价下排斥自身质量
- 异常样本因位于低密度区需大幅移动，导致更高运输成本
- 适用于无监督异常检测，尤其适合工业故障识别场景
在机器学习中，异常检测是一个长期存在的问题。异常被定义为与数据整体显著偏离的样本。最优传输（OT）是数学中研究两个概率测度间以最小代价进行运输的问题。经典OT中，一个测度向自身运输的最优策略是恒等映射。本文提出一种新方法：通过强制样本排斥其自身质量，同时保持最小运输代价，构建新的运输问题——质量排斥最优传输（MROT）。由于低密度区域的样本必须大幅移动才能满足排斥要求，因此会产生更高的运输成本。利用这一特性，我们设计了一种新型异常评分机制。在多个基准数据集和故障检测任务中的实验表明，该方法优于现有技术。
原文摘要 · Abstract (English)
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.
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