Graph learning under sparsity priors

TL;DR

This paper introduces a method for inferring graph structures from signals by leveraging sparsity priors and structured graph dictionaries, enabling effective recovery of underlying networks from observed data.

Contribution

It proposes a novel graph learning approach based on sparse representations with polynomial Laplacian dictionaries, addressing the challenge of unknown data structures.

Findings

Good graph recovery performance demonstrated

Method compares favorably to recent algorithms

Effective in inferring networks from signals

Abstract

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred from the mere signal observations. This is exactly the problem that we address in this paper, under the assumption that the graph signals can be represented as a sparse linear combination of a few atoms of a structured graph dictionary. The dictionary is constructed on polynomials of the graph Laplacian, which can sparsely represent a general class of graph signals composed of localized patterns on the graph. We formulate a graph learning problem, whose solution provides an ideal fit between the signal observations and the sparse graph signal model. As the problem is non-convex, we propose to solve it by alternating between a signal sparse coding and a graph update step. We provide experimental results that outline the good graph recovery performance of our method, which generally compares favourably to other recent network inference algorithms.