Smoothing graph signals via random spanning forests

Yusuf Yigit Pilavci (1) , Pierre-Olivier Amblard (1) , Simon Barthelme (1) , Nicolas Tremblay (1)

1 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes

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.

Mots clés: smoothing; random spanning forests; graph signal processing

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

Yusuf Yigit Pilavci, Pierre-Olivier Amblard, Simon Barthelme, Nicolas Tremblay. Smoothing graph signals via random spanning forests. ICASSP 2020 - IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE, May 2020, Barcelone (virtual), Spain. ⟨10.1109/ICASSP40776.2020.9054497⟩. ⟨hal-02319175v2⟩