http://orcid.org/0000-0003-3312-8222
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Abstract
Graph analytics methods have evoked significant interest in recent years. Their applicability to real-world complex systems is currently limited by the challenges of inferring effective graph representations of the high-dimensional, noisy, nonlinear and transient dynamics from limited time series outputs, as well as of extracting statistical quantifiers that capture the salient structure of the inferred graphs for detecting change. In this article, we present an approach to detecting changes in complex dynamic systems that is based on spectral-graph-theory and uses a single realization of time series data collected under specific, common types of transient conditions, such as intermittency. We introduce a statistic, γk, based on the spectral content of the inferred graph. We show that the γk statistic under high-dimensional dynamics converges to a normal distribution, and we employ the parameters of this distribution to construct a procedure to detect qualitative changes in the coupling structure of a dynamical system. Experimental investigations suggest that the γk statistic by itself is able to detect changes with modified area under curve (mAUC) of about 0.96 (for numerical simulation tests), and can, by itself, achieve a true positive rate of about 40% for detecting seizures from EEG signals. In addition, by incorporating this statistic with random forest, one of the best seizure detection methods, the seizure detection rate of the random forest method improves by 5% in 35% of the subjects. These studies of the network inferred from EEG signals suggest that γk can capture salient structural changes in the physiology of the process and can therefore serve as an effective feature for detecting seizures from EEG signals.
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Hoang M. Tran
Hoang M. Tran received his Ph.D. degree in industrial and systems engineering from Texas A&M University, College Station, TX, and his BS. & MS. in applied mathematics from Hanoi University of Science and Technology in Vietnam. He is currently working as a data scientist at Esmart Systems AS, Halden, Norway. He is working on developing IoT based solutions for smart grid/power systems. His research interestes are on machine learning, mathematical modelling and game theory.
Satish T. S. Bukkapatnam
Satish T. S. Bukkapatnam received his Ph.D. degree in industrial and manufacturing engineering from Pennsylvania State University. He currently serves as Rockwell International Professor with Department of Industrial and Systems Engineering department at Texas A&M University, College Station, TX. He is also the Director of Texas A&M Engineering Experimentation Station (TEES) Institute for Manufacturing Systems, and has joint appointments with Biomedical and Mechanical Engineering departments. His research addresses the harnessing of high-resolution nonlinear dynamic information, especially from wireless MEMS sensors, to improve the monitoring and prognostics, mainly of ultraprecision and nanomanufacturing processes and machines, and cardiorespiratory processes. His research has led to 151 peer-reviewed publications; five pending patents; $5 million in grants as PI/Co-PI from the National Science Foundation, the U.S. Department of Defense, and the private sector; and 14 best-paper/poster recognitions. He is a fellow of the Institute for Industrial and Systems Engineers (IISE), and the Society of Manufacturing Engineers (SME).
Mridul Garg
Mridul Garg received his MS. degree in industrial and systems engineering from Texas A&M University, College Station, TX. He is currently working as a Data Scientist at Dell, Austin, USA.