大数据中孤立树异常点检测方法的数学评价
A Mathematical Assessment of the Isolation Tree Method for Outliers Detection in Big Data
摘要：
本文对孤立随机森林法进行了数学分析。我们表明，IRF空间可以赋予一个概率引起的隔离树算法（iTree）。在这种情况下，IRF方法的收敛性证明使用大数定律。本文通过几个反例说明了原方法在检测异常时是不确定的，不能给出质量证明。因此，IRF的一个替代版本的建议，其数学基础，以及其局限性，是完全合理的。最后通过数值实验比较了经典IRF和新IRF的性能。
英文摘要：
In this paper, the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection is presented. We show that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved using the Law of Large Numbers. A couple of counterexamples are presented to show that the original method is inconclusive and no quality certificate can be given, when using it as a means to detect anomalies. Hence, an alternative version of IRF is proposed, whose mathematical foundation, as well as its limitations, are fully justified. Finally, numerical experiments are presented to compare the performance of the classic IRF with the proposed one.
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