Smoothing graph signals via random spanning forests

TL;DR

This paper introduces novel Monte-Carlo estimators for graph signal smoothing based on random spanning forests, with efficient sampling and theoretical variance analysis, applicable to denoising and semi-supervised learning on graphs.

Contribution

It proposes new estimators leveraging random spanning forests for graph signal smoothing, with efficient sampling methods and variance analysis, advancing graph signal processing techniques.

Findings

Efficient linear-time sampling of random spanning forests.

Theoretical variance bounds for the estimators.

Successful application to denoising and semi-supervised learning.

Abstract

Another facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These random forests are sampled efficiently via a variant of Wilson's algorithm --in time linear in the number of edges. The theoretical variance of the proposed estimators are analyzed, and their application to several problems are considered, such as Tikhonov denoising of graph signals or semi-supervised learning for node classification on graphs.