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

Abstract

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

11 pages, 5 figures

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Cited by in corpus (8)

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• Graphon Signal Processing
• Bayesian Estimation of Graph Signals
• Unifying Graph Convolution and Contrastive Learning in Collaborative Filtering
• Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis
• Blind Graph Matching Using Graph Signals
• Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation
• Learning Graph Filters for Structure-Function Coupling based Hub Node Identification