Stochastic processes on graphs: learning representations and applications

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dc.contributor.advisorBalan, Radu Ven_US
dc.contributor.authorBohannon, Addison Woodforden_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2019-06-20T05:34:36Z
dc.date.available2019-06-20T05:34:36Z
dc.date.issued2019en_US
dc.description.abstractIn this work, we are motivated by discriminating multivariate time-series with an underlying graph topology. Graph signal processing has developed various tools for the analysis of scalar signals on graphs. Here, we extend the existing techniques to design filters for multivariate time-series that have non-trivial spatiotemporal graph topologies. We show that such a filtering approach can discriminate signals that cannot otherwise be discriminated by competing approaches. Then, we consider how to identify spatiotemporal graph topology from signal observations. Specifically, we consider a generative model that yields a bilinear inverse problem with an observation-dependent left multiplication. We propose two algorithms for solving the inverse problem and provide probabilistic guarantees on recovery. We apply the technique to identify spatiotemporal graph components in electroencephalogram (EEG) recordings. The identified components are shown to discriminate between various cognitive task conditions in the data.en_US
dc.identifierhttps://doi.org/10.13016/uepm-xw8h
dc.identifier.urihttp://hdl.handle.net/1903/21986
dc.language.isoenen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pquncontrolleddictionary learningen_US
dc.subject.pquncontrolledfunctional calculusen_US
dc.subject.pquncontrolledfunctional connectivityen_US
dc.subject.pquncontrolledgraph theoryen_US
dc.subject.pquncontrolledsignal processingen_US
dc.subject.pquncontrolledstochastic processesen_US
dc.titleStochastic processes on graphs: learning representations and applicationsen_US
dc.typeDissertationen_US

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