Graph Learning Under Spectral Sparsity Constraints

Subbareddy, B. and Siripuram, Aditya and Zhang, Jingxin (2021) Graph Learning Under Spectral Sparsity Constraints. In: 2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021, 6 June 2021 through 11 June 2021, Virtual,Toronto.

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Abstract

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a case for inferring graphs on which the observed data has high variation. We propose a new signal processing based inference model and a new learning criterion that allow for wideband frequency variation in the data and derive an algorithm for graph inference. The proposed inference algorithm consists of two steps: 1) learning orthogonal eigenvectors of a graph from the data; 2) recovering the adjacency matrix of the graph topology from the given graph eigenvectors. The first step is solved by an iterative algorithm with a closed-form solution. In the second step, the adjacency matrix is inferred from the eigenvectors by solving a convex optimization problem. Numerical results on synthetic data show the proposed inference algorithm can effectively capture the meaningful graph topology from observed data under the wideband assumption. © 2021 IEEE

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