Identifying the Topology of Undirected Networks From Diffused Non-Stationary Graph Signals

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dc.citation.firstpage171en_US
dc.citation.journalTitleIEEE Open Journal of Signal Processingen_US
dc.citation.lastpage189en_US
dc.citation.volumeNumber2en_US
dc.contributor.authorShafipour, Rasoulen_US
dc.contributor.authorSegarra, Santiagoen_US
dc.contributor.authorMarques, Antonio G.en_US
dc.contributor.authorMateos, Gonzaloen_US
dc.date.accessioned2022-04-15T14:45:19Zen_US
dc.date.available2022-04-15T14:45:19Zen_US
dc.date.issued2021en_US
dc.description.abstractWe address the problem of inferring an undirected graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the unknown network. Using the so-called graph-shift operator (GSO), which is a matrix representation of the graph, we first identify the eigenvectors of the shift matrix from observations of the diffused signals, and then estimate the eigenvalues by imposing desirable properties on the graph to be recovered. Different from the stationary setting where the eigenvectors can be obtained directly from the covariance matrix of the measurements, here we need to estimate first the unknown diffusion (graph) filter - a polynomial in the GSO that preserves the sought eigenbasis. To carry out this initial system identification step, we exploit different sources of information on the arbitrarily-correlated input signal driving the diffusion on the graph. We first explore the setting where the observations, the input information, and the unknown graph filter are linearly related. We then address the case where the relation is given by a system of matrix quadratic equations, which arises in pragmatic scenarios where only the second-order statistics of the inputs are available. While such a quadratic filter identification problem boils down to a non-convex fourth-order polynomial minimization, we discuss identifiability conditions, propose algorithms to approximate the solution, and analyze their performance. Numerical tests illustrate the effectiveness of the proposed topology inference algorithms in recovering brain, social, financial, and urban transportation networks using synthetic and real-world signals.en_US
dc.identifier.citationShafipour, Rasoul, Segarra, Santiago, Marques, Antonio G., et al.. "Identifying the Topology of Undirected Networks From Diffused Non-Stationary Graph Signals." <i>IEEE Open Journal of Signal Processing,</i> 2, (2021) IEEE: 171-189. https://doi.org/10.1109/OJSP.2021.3063926.en_US
dc.identifier.digitalIdentifying_the_Topology_of_Undirected_Networksen_US
dc.identifier.doihttps://doi.org/10.1109/OJSP.2021.3063926en_US
dc.identifier.urihttps://hdl.handle.net/1911/112074en_US
dc.language.isoengen_US
dc.publisherIEEEen_US
dc.rightsThis work is licensed under a Creative Commons Attribution 4.0 License.en_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en_US
dc.titleIdentifying the Topology of Undirected Networks From Diffused Non-Stationary Graph Signalsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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