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A User Guide to Low-Pass Graph Signal Processing and its Applications

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Document pages: 11 pages

Abstract: The notion of graph filters can be used to define generative models for graphdata. In fact, the data obtained from many examples of network dynamics may beviewed as the output of a graph filter. With this interpretation, classicalsignal processing tools such as frequency analysis have been successfullyapplied with analogous interpretation to graph data, generating new insightsfor data science. What follows is a user guide on a specific class of graphdata, where the generating graph filters are low-pass, i.e., the filterattenuates contents in the higher graph frequencies while retaining contents inthe lower frequencies. Our choice is motivated by the prevalence of low-passmodels in application domains such as social networks, financial markets, andpower systems. We illustrate how to leverage properties of low-pass graphfilters to learn the graph topology or identify its community structure;efficiently represent graph data through sampling, recover missingmeasurements, and de-noise graph data; the low-pass property is also used asthe baseline to detect anomalies.

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