Signal processing on graphs: Performance of graph structure estimation

Abstract

A class of models for describing sets of time series generated by interacting agents using directed, weighted graphs is introduced. A computationally tractable algorithm for estimating the graph adjacency matrix of this model from observed time series data is presented. The performance guarantees of this algorithm for prediction are outlined under several assumptions on the properties of the dynamics of the system of agents and on the true values of the parameters. These guarantees are tested empirically through simulation studies using several random graph models.

Graph learning under sparsity priors

“…The recent framework in [12] that observes graph signals as white signals filtered with a graph shift operator polynomial, is one of the first network inference works to depart from explicit global smoothness assumptions. A similar idea uses adjacency matrix polynomials to model causation in time-varying signals [13], [14].…”

New results on multi-agent system consensus: A graph signal processing perspective

“…are two different frameworks on graph signal processing. One develops the discrete signal processing structure and concepts on graph based on the Jordan normal form and generalized eigenbasis of the adjacency matrix [11][12][13][14][15]. The other establishes the framework by merging algebraic and spectral graph concepts with classical signal processing which interprets the graph Laplacian eigenvalues as graph frequencies and the orthonormal eigenvectors as graph Fourier transformation [10,[16][17][18][19].…”