2020/04/09 by Fernando A. Morales, Morales, Fernando A., Jorge Ramírez +3
Computer Science · Engineering · #65C05 #68U01 #68W20 #Anomaly Detection Techniques and Applications #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Network Security and Intrusion Detection #Neural Networks and Applications #Probability (math.PR) #Water Systems and Optimization
paper · pdf · doi:10.48550/arxiv.2004.04512
openalex publication_date 2020/04/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, the mathematical analysis of the Isolation Random Forest\nMethod (IRF Method) for anomaly detection is presented. We show that the IRF\nspace can be endowed with a probability induced by the Isolation Tree algorithm\n(iTree). In this setting, the convergence of the IRF method is proved using the\nLaw of Large Numbers. A couple of counterexamples are presented to show that\nthe original method is inconclusive and no quality certificate can be given,\nwhen using it as a means to detect anomalies. Hence, an alternative version of\nIRF is proposed, whose mathematical foundation, as well as its limitations, are\nfully justified. Finally, numerical experiments are presented to compare the\nperformance of the classic IRF with the proposed one.\n