For the purpose of monitoring the behavior of complex infrastructures (e.g. aircrafts, transport or energy networks), high-rate sensors are deployed to capture multivariate data, generally unlabeled, in quasi continuous-time to detect quickly the occurrence of anomalies that may jeopardize the smooth operation of the system of interest. The statistical analysis of such massive data of functional nature raises many challenging methodological questions. The primary goal of this paper is to extend the popular Isolation Forest (IF) approach to Anomaly Detection, originally dedicated to finite dimensional observations, to functional data. The major difficulty lies in the wide variety of topological structures that may equip a space of functions and the great variety of patterns that may characterize abnormal curves. We address the issue of (randomly) splitting the functional space in a flexible manner in order to isolate progressively any trajectory from the others, a key ingredient to the efficiency of the algorithm. Beyond a detailed description of the algorithm, computational complexity and stability issues are investigated at length. From the scoring function measuring the degree of abnormality of an observation provided by the proposed variant of the IF algorithm, a Functional Statistical Depth function is defined and discussed as well as a multivariate functional extension. Numerical experiments provide strong empirical evidence of the accuracy of the extension proposed.
Function Based Isolation Forest (FuBIF): A Unifying Framework for Interpretable Isolation-Based Anomaly Detection
Brain, Mind and Computer Science, University of Padova, Italy（脑科学与计算机科学系，帕多瓦大学，意大利）；Department of Mathematics, Sapienza University of Roma, Italy（数学系，罗马萨皮恩扎大学，意大利）；Department of Information Engineering, University of Padova, Italy（信息工程系，帕多瓦大学，意大利）
Institut Pasteur（巴斯德研究所）；Université Paris Cité（巴黎城市大学）；Inserm（法国国家健康与医学研究院）；Institut de l’Audition（听觉研究所）；IHU reConnect（reConnect 医院研究所）；INRIA（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；Univ. Paris-Saclay（巴黎-萨克雷大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）；Institute of Statistical Mathematics（统计数学研究所）
Preference Isolation Forest for Structure-based Anomaly Detection
Department of Electronics, Information and Bioengineering, Politecnico di Milano（电子、信息与生物工程系，米兰理工大学）；Faculty of Informatics, Università della Svizzera Italiana（信息技术学院，意大利瑞士大学）
OptIForest: Optimal Isolation Forest for Anomaly Detection
Macquarie University（麦考瑞大学）；CSIRO’s Data61（联邦科学与工业研究组织数据61研究所）；Qufu Normal University（曲阜师范大学）；Nanjing University（南京大学）；Nanjing University of Information Science and Technology（南京信息工程大学）
Isolation-based Spherical Ensemble Representations for Tabular Anomaly Detection
Tsinghua Shenzhen International Graduate School, Tsinghua University, China（清华大学深圳国际研究生院，清华大学，中国）；School of Computing and Information Technology, Great Bay University, China（计算机与信息科技学院，Great Bay大学，中国）；School of Compuer Science, Nanjing University, China（计算机科学学院，南京大学，中国）；Computer department, Dongguan university of technology, China（计算机系，东莞科技学院，中国）；College of Computer Science and Technology, China University of Petroleum, China（计算机科学与技术学院，中国石油大学，中国）；School of IT, Deakin University, Australia（信息技术学院，德金大学，澳大利亚）
A Classifier-Based Approach to Multi-Class Anomaly Detection Applied to Astronomical Time-Series
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所）；Irvington High School（欧文顿高中）；Department of Physics and Astronomy, University of the Western Cape（西开普大学物理与天文学系）；South African Radio Astronomy Observatory（南非射电天文观测台）
Theoretical Investigation on Inductive Bias of Isolation Forest
National Key Laboratory for Novel Software Technology, Nanjing University, China（新型软件技术国家实验室，南京大学）；School of Artificial Intelligence, Nanjing University, China（人工智能学院，南京大学）；School of Intelligence Science and Technology, Nanjing University, China（智能科学与技术学院，南京大学）；College of Computer and Information, Hohai University, China（计算机与信息学院，河海大学）；Key Laboratory of Water Resources Big Data Technology of Ministry of Water Resources, Hohai University, China（水利部水资源大数据技术重点实验室，河海大学）
Enhancing Visual Interpretability and Explainability in Functional Survival Trees and Forests
Department of Mathematics and Physics, University of Campania Luigi Vanvitelli（数学与物理系，坎帕尼亚卢igi vanvitelli大学）；Department of Economics, Statistics and Business, Universitas Mercatorum（经济学、统计学与商业系，默卡托鲁姆大学）
Signed iterative random forests to identify enhancer-associated transcription factor binding
University of California, San Francisco（加州大学旧金山分校）；Cornell University（康奈尔大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）
Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations
Faculty of Technological and Innovation Sciences（技术与创新科学学院）；Faculty of Economics and Law（经济与法学院）
Functional Random Forest with Adaptive Cost-Sensitive Splitting for Imbalanced Functional Data Classification
Fahad Mostafa School of Mathematical and Natural Sciences, Arizona State University, USA（法哈德·莫斯塔法 数学与自然科学学院，亚利桑那州立大学）；Hafiz Khan Department of Public Health, Julia Jones Matthews School of Population and Public Health, Texas Tech Health Sciences Center, USA（哈菲兹·汗 公共卫生部，朱莉亚·琼斯·马修斯流行病学与公共卫生学院，德克萨斯技术健康科学中心）
