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Signal Processing on Directed Graphs

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Document pages: 14 pages

Abstract: This paper provides an overview of the current landscape of signal processing(SP) on directed graphs (digraphs). Directionality is inherent to manyreal-world (information, transportation, biological) networks and it shouldplay an integral role in processing and learning from network data. We thus layout a comprehensive review of recent advances in SP on digraphs, offeringinsights through comparisons with results available for undirected graphs,discussing emerging directions, establishing links with related areas inmachine learning and causal inference in statistics, as well as illustratingtheir practical relevance to timely applications. To this end, we begin bysurveying (orthonormal) signal representations and their graph frequencyinterpretations based on novel measures of signal variation for digraphs. Wethen move on to filtering, a central component in deriving a comprehensivetheory of SP on digraphs. Indeed, through the lens of filter-based generativesignal models, we explore a unified framework to study inverse problems (e.g.,sampling and deconvolution on networks), statistical analysis of randomsignals, and topology inference of digraphs from nodal observations.

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