Detecting changes in transient complex systems via dynamic network inference

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.