Optimal Filter Design for Signal Processing on Random Graphs: Accelerated Consensus - 2018


In graph Signal Processing, filters arise from polynomials in shift matrices that respect the graph structure, such as the graph adjacency matrix or the graph Laplacian matrix. Hence, filter design for graph Signal Processing benefits from knowledge of the spectral decomposition of those matrices. Usually, stochastic influences affect the network structure and, consequently, the shift matrix empirical spectral distribution. Although the joint distribution of the shift matrix eigenvalues is usually inaccessible, deterministic functions that asymptotically approximate the matrix empirical spectral distribution can be found for suitable random graph models using tools from random matrix theory. We employ this info concerning the density of eigenvalues to develop criteria for optimal graph filter design. In particular, we have a tendency to consider filter design for distributed average consensus and connected problems, leading to enhancements in brief-term error minimization or in asymptotic convergence rate.

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