Abstract
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a corresponding optimization problem. We provide a general solution by using the alternating direction methods of multipliers. We next show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery, and provide corresponding specific solutions and theoretical analysis. Finally, we validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system, and expert opinion combination of online blog classification.
Highlights
With the explosive growth of information and communication, signals are being generated at an unprecedented rate from various sources, including social networks, citation, biological, and physical infrastructures [1], [2]
The second approach, discrete signal processing on graphs (DSPG) [3], [4], is rooted in the algebraic signal processing theory [26], [27] and builds on the graph shift operator, which works as the elementary filter that generates all linear shift-invariant filters for signals with a given structure
We propose a graph signal model, cast graph signal recovery as an optimization problem, and provide a general solution by using the alternating direction method of multipliers
Summary
With the explosive growth of information and communication, signals are being generated at an unprecedented rate from various sources, including social networks, citation, biological, and physical infrastructures [1], [2]. Two basic approaches to signal processing on graphs have been considered, both of which analyze signals with complex, irregular structure, generalizing a series of concepts and tools from classical signal processing, such as graph filters, or graph Fourier transform, to diverse graph-based applications, such as graph signal denoising, compression, classification, and clustering [5], [21]–[23]. Since the graph Laplacian matrix is restricted to be symmetric and positive semi-definite, this approach is applicable only to undirected graphs with real and nonnegative edge weights. Since the graph shift operator is not restricted to be symmetric, this approach is applicable to arbitrary graphs, those with undirected or directed edges, with real or complex, nonnegative or negative weights
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