Abstract:
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Abstract: Most recently, the tools of geometric deep learning (GDL) and, in particular, graph neural networks emerge as a promising new alternative in unsupervised anomaly detection problems where the data exhibit a sophisticated nonlinear dependence structure such as various geospatial surveillance systems. However, prevailing GDL-based methods for anomaly detection tend to exhibit limited capabilities to capture multi-scale spatio-temporal variability which is ubiquitous in many applications, particularly, related to biosurveillance and biothreats. Motivated by the problem of assessing COVID-19 severity, we develop a novel approach to unsupervised anomaly detection in spatio-temporal data by fusing the notion of GDL with the emerging direction of persistent homologies and topological data analysis. In particular, our key idea is to bolster the GDL performance by leveraging the complementary insight on the intrinsic multi-scale data organization which topological descriptors can provide. We show the utility of the new approach to detecting, forecasting and interpreting risks in COVID-19 clinical severity, measured in terms of hospitalization rates, in three U.S. states.
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