Compared to theoretical frameworks that assume equal sensitivity to deviations in all features of data, the theory of anomaly detection allowing for variable sensitivity across features is less developed. To the best of our knowledge, this issue has not yet been addressed in the context of isolation-based methods, and this paper represents the first attempt to do so. This paper introduces an Extended Isolation Forest with feature sensitivities, which we refer to as the Anisotropic Isolation Forest (AIF). In contrast to the standard EIF, the AIF enables anomaly detection with controllable sensitivity to deviations in different features or directions in the feature space. The paper also introduces novel measures of directional sensitivity, which allow quantification of AIF's sensitivity in different directions in the feature space. These measures enable adjustment of the AIF's sensitivity to task-specific requirements. We demonstrate the performance of the algorithm by applying it to synthetic and real-world datasets. The results show that the AIF enables anomaly detection that focuses on directions in the feature space where deviations from typical behavior are more important.

翻译：相较于假设数据所有特征偏差具有同等敏感性的理论框架，允许不同特征间敏感性可变的异常检测理论发展尚不充分。据我们所知，该问题在基于隔离的方法中尚未得到解决，本文是首次尝试。本文提出了一种具有特征敏感性的扩展隔离森林，我们称之为各向异性隔离森林（AIF）。与标准EIF相比，AIF能够实现对特征空间中不同特征或方向偏差的可控敏感性异常检测。本文还提出了新颖的方向敏感性度量方法，可量化AIF在特征空间不同方向上的敏感性。这些度量使得AIF的敏感性能够根据特定任务需求进行调整。我们通过合成数据集和真实世界数据集验证了算法性能。结果表明，AIF能够实现专注于特征空间中偏离典型行为更显著方向的异常检测。