@article{cdf791778bf34f03ac06ca066e617f70,
title = "Generalized support vector data description for anomaly detection",
abstract = "Traditional anomaly detection procedures assume that normal observations are obtained from a single distribution. However, due to the complexities of modern industrial processes, the observations may belong to multiple operating modes with different distributions. In such cases, traditional anomaly detection procedures may trigger false alarms while the process is indeed in another normally operating mode. We propose a generalized support vector-based anomaly detection procedure called generalized support vector data description which can be used to determine the anomalies in multimodal processes. The proposed procedure constructs hyperspheres for each class in order to include as many observations as possible and keep other class observations as far apart as possible. In addition, we introduce a generalized Bayesian framework which does not only consider the prior information from each mode, but also highlights the relationships among the modes. The effectiveness of the proposed procedure is demonstrated through various simulation studies and real-life applications.",
keywords = "Anomaly detection, Bayesian statistics, Multimode process, Support vector data description",
author = "Mehmet Turkoz and Sangahn Kim and Youngdoo Son and Jeong, {Myong K.} and Elsayed, {Elsayed A.}",
note = "Funding Information: Eq. (13) Starting with (11) , (B.1) ⌢ α = arg max α ln ( p ( α | D ) ) = arg max α ln ( p ( D | α ) p ( α ) ) = arg max α [ ln ( p ( D | α ) ) + ln ( p ( α ) ) ] Two terms in (B.1) can be written as p ( α ) = ( ∏ i = 1 n p ( α ( i ) ) ) ( ∏ i = 1 n ∏ j = 1 n p ( β ( i , j ) ) ) = ( 1 ( 2 π ) 1 2 ∑ i = 1 n N i σ ∑ i = 1 n N i ) e − 1 2 σ 2 ∑ i = 1 n ∥ α ( i ) − m ( i ) ∥ 2 2 × ( 1 ( 2 π ) ∑ i = 1 n N i σ 2 ∑ i = 1 n N i ) e − 1 2 σ 2 ∑ i = 1 n ∑ j = 1 n ∥ β ( i , j ) − m ( i , j ) ∥ 2 2 ln ( p ( α ) ) = ln ( 1 ( 2 π ) 3 2 ∑ i = 1 n N i σ 3 ∑ i = 1 n N i ) − 1 2 σ 2 [ ( ∑ i = 1 n α ( i ) T α ( i ) − 2 α ( i ) T m ( i ) + m ( i ) T m ( i ) ) + ( ∑ i = 1 n ∑ i ≠ j = 1 n β ( i , j ) T β ( i , j ) − 2 β ( i , j ) T m ( i , j ) + m ( i , j ) T m ( i , j ) ) ] The results of ln ( p ( D | α ))and ln ( p ( α )) are substituted in (B.1) . Therefore, (13) is obtained as follows: ⌢ α = arg max α 2 − 1 [ 2 ∑ m = 1 n σ m m − 2 ( α ( m ) ) T B ( m ) 1 ( m ) − 2 ∑ m = 1 n ∑ m ≠ k = 1 n σ k k − 2 ( β ( m , k ) ) T B ( m , k ) 1 ( m , k ) − ∑ k = 1 n N k σ k k − 2 ( α ( k ) ) T K ( k ) α ( k ) − ∑ m = 1 n ∑ m ≠ k = 1 n N m σ m m − 2 ( β ( k , m ) ) T K ( k ) β ( k , m ) + 2 ∑ m = 1 n ∑ m ≠ k = 1 n N m σ m m − 2 ( α ( m ) ) T K ( m , k ) β ( k , m ) − σ − 2 ( ∑ i = 1 n α ( i ) T α ( i ) − 2 α ( i ) T m ( i ) ) − σ − 2 ( ∑ i = 1 n ∑ i ≠ j = 1 n β ( i , j ) T β ( i , j ) − 2 β ( i , j ) T m ( i , j ) ) ] Mehmet Turkoz is currently an Assistant Professor of Professional Practice in the Department of Management Science and Information Systems, Rutgers University, USA. He received his PhD from the Department of Industrial and Systems Engineering, Rutgers University, USA in 2018. He holds an MS degree in Operations Research from Rutgers University, USA, in 2012. His research areas include data mining, machine learning, process modeling and monitoring, and operations research. Sangahn Kim is currently an Assistant Professor in the Department of Business Analytics and Actuarial Science, Siena College, USA. He received his Ph.D. from the Department of Industrial and Systems Engineering, Rutgers University, USA. He is a recipient of the Richard A. Freund International Scholarship by American Society for Quality (ASQ) in 2016. He also won the Best PhD Student Award and the Tayfur Altiok Memorial Scholarship from Rutgers University. His research interests include data analytics, process modeling and monitoring, stochastic process, reliability engineering, statistical learning, and machine learning. Youngdoo Son is an Assistant Professor in the Department of Industrial and Systems Engineering, Dongguk University (Seoul campus), Seoul, South Korea. He received B.S. in Physics and M.S. in Industrial and Management Engineering from Pohang University of Science and Technology (POSTECH), Pohang, South Korea in 2010 and 2012, respectively, and his Ph.D. in Industrial Engineering from Seoul National University, South Korea in 2015. His research interests include machine learning, neural networks, Bayesian methods, and their industrial and business applications. Myong K. (MK) Jeong is a Professor in the Department of Industrial and Systems Engineering and RUTCOR (Rutgers Center for Operation Research), Rutgers University, New Brunswick, New Jersey. His research interests include machine learning, data mining, stochastic processes, sensor data analysis, statistical learning, and big data. He received the prestigious Richard A. Freund International Scholarship by ASQ and the National Science Foundation (NSF) CAREER Award in 2002 and 2007, respectively. His research has been funded by the NSF, United States Department of Agriculture (USDA), National Transportation Research Center, Inc. (NTRCI), and industry. He has been a consultant for Samsung Electronics, Intel, ETRI, and other companies. He has published more than 90 refereed journal articles. He has served as an Associate Editor of several journals such as the IEEE Transaction on Automation Science and Engineering, International Journal of Advanced Manufacturing Technology, and International Journal of Quality, Statistics and Reliability. Elsayed A. Elsayed is a Distinguished Professor in the Department of Industrial and Systems Engineering, Rutgers, The State University of New Jersey. His research interests are in the areas of quality and reliability engineering. He is the author of Reliability Engineering, John Wiley & Sons, 2012. He is the author and coauthor of work published in IIE Transactions, IEEE Transactions, and the International Journal of Production Research. His research has been funded by the DoD, FAA, NSF, and industry. Dr. Elsayed has been a consultant for DoD, AT&T Bell Laboratories, Ingersoll-Rand, Johnson & Johnson, Personal Products, AT&T Communications, Ethicon and other companies. Dr. Elsayed was the Editor-in-Chief of IIE Transactions and the Editor of IIE Transactions on Quality and Reliability Engineering. He is also an Editor for the International Journal of Reliability, Quality and Safety Engineering. Publisher Copyright: {\textcopyright} 2019",
year = "2020",
month = apr,
doi = "10.1016/j.patcog.2019.107119",
language = "English (US)",
volume = "100",
journal = "Pattern Recognition",
issn = "0031-3203",
publisher = "Elsevier Limited",
}