Anomaly detection plays an increasingly important role in various fields for
critical tasks such as intrusion detection in cybersecurity, financial risk
detection, and human health monitoring. A variety of anomaly detection methods
have been proposed, and a category based on the isolation forest mechanism
stands out due to its simplicity, effectiveness, and efficiency, e.g., iForest
is often employed as a state-of-the-art detector for real deployment. While the
majority of isolation forests use the binary structure, a framework LSHiForest
has demonstrated that the multi-fork isolation tree structure can lead to
better detection performance. However, there is no theoretical work answering
the fundamentally and practically important question on the optimal tree
structure for an isolation forest with respect to the branching factor. In this
paper, we establish a theory on isolation efficiency to answer the question and
determine the optimal branching factor for an isolation tree. Based on the
theoretical underpinning, we design a practical optimal isolation forest
OptIForest incorporating clustering based learning to hash which enables more
information to be learned from data for better isolation quality. The rationale
of our approach relies on a better bias-variance trade-off achieved by bias
reduction in OptIForest. Extensive experiments on a series of benchmarking
datasets for comparative and ablation studies demonstrate that our approach can
efficiently and robustly achieve better detection performance in general than
the state-of-the-arts including the deep learning based methods.

本研究旨在回答孤立森林隔离效率的理论最优分支因子，并通过偏差减少实现更好的偏差 - 方差权衡，提出一种 OptIForest 算法，结合基于聚类的哈希学习，以实现更好的隔离效果、更高效且更具鲁棒性。在一系列基准数据集上的实验表明，该方法普遍优于深度学习等现有方法。