Nonparametric Anomaly Detection on Time Series of Graphs

Abstract

Identifying change points and/or anomalies in dynamic network structures has become increasingly popular across various domains, from neuroscience to telecommunication to finance. One of the particular objectives of the anomaly detection task from the neuroscience perspective is the reconstruction of the dynamic manner of brain region interactions. However, most statistical methods for detecting anomalies have the following unrealistic limitation for brain studies and beyond: that is, network snapshots at different time points are assumed to be independent. To circumvent this limitation, we propose a distribution-free framework for anomaly detection in dynamic networks. First, we present each network snapshot of the data as a linear object and find its respective univariate characterization via local and global network topological summaries. Second, we adopt a change point detection method for (weakly) dependent time series based on efficient scores, and enhance the finite sample properties of change point method by approximating the asymptotic distribution of the test statistic using the sieve bootstrap. We apply our method to simulated and to real data, particularly, two functional magnetic resonance imaging (fMRI) datasets and the Enron communication graph. We find that our new method delivers impressively accurate and realistic results in terms of identifying locations of true change points compared to the results reported by competing approaches. The new method promises to offer a deeper insight into the large-scale characterizations and functional dynamics of the brain and, more generally, into intrinsic structure of complex dynamic networks.

Cross-covariance isolate detect: a new change-point method for estimating dynamic functional connectivity

“…There is no software available for BO, which is also the case for the majority of the methods mentioned in the introduction. However, for the BO approach, code was provided to us by the authors, which we had to adjust through a function that has already been written for the simulations carried out in Ofori-Boateng et al (2020). For SBS, we only present the results for the finer scale of −1 used in the wavelet transformation.…”

“…Finally, Ofori-Boateng et al (2020) introduced a new method that firstly presents each network snapshot of fMRI data as a linear object and finds its respective univariate characterization via local and global network topological summaries and then adopts a change-point detection method for (weakly) dependent time series based on efficient scores.…”

“…Functional connectivity (FC) is the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Evidence of the non stationary behavior of FC (or FC networks) has been observed in high temporal resolution electroencephalography (EEG) data, task based fMRI experiments (Fox et al, 2005; Debener et al, 2006; Cribben et al, 2012, 2013) and even prominently in resting state fMRI data (Delamillieure et al, 2010; Doucet et al, 2012; Cribben & Yu, 2017; Ofori-Boateng et al, 2020). By estimating a FC network across the entire experimental time course, the resulting FC network is simply an average of the changing connectivity structures.…”

“…More recently, Kundu et al (2018) proposed a fully automated two-stage approach which pools information across multiple subjects to estimate change-points in functional connectivity, while Dai et al (2019) developed a formal statistical test for finding change-points in time series associated with FC. Finally, Ofori-Boateng et al (2020) introduced a new method that firstly presents each network snapshot of fMRI data as a linear object and finds its respective univariate characterization via local and global network topological summaries and then adopts a change-point detection method for (weakly) dependent time series based on efficient scores.…”

Development of a Model for Water Scrubbing‐Based Biogas Upgrading and Biomethane Compression

“…Biogas is produced by anaerobic digestion of agricultural byproducts, animal manure, and slurry [1]. Its composition depends strongly on the organic substrate and the digestion conditions [2].…”