Graph Tikhonov Regularization and Interpolation 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

Novel Monte Carlo estimators are proposed to solve both the Tikhonov regularization (TR) and the interpolation problems on graphs. These estimators are based on random spanning forests (RSF), the theoretical properties of which enable to analyze the estimators' theoretical mean and variance. We also show how to perform hyperparameter tuning for these RSF-based estimators. Finally, TR or interpolation being a building block of several algorithms, we show how the proposed estimators can be easily adapted to avoid expensive intermediate steps in well-known algorithms such as generalized semi-supervised learning, label propagation, Newton's method and iteratively reweighted least square. In the experiments, we illustrate the proposed methods on several problems and provide observations on their run time, which are comparable with the state-of-the-art.

Mots clés: interpolation; smoothing; random spanning forests; graph signal processing; Index Terms-graph signal processing; IRLS; newton's method; label propagation; semi-supervised learning

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

Yusuf Yigit Pilavci, Pierre-Olivier Amblard, Simon Barthelme, Nicolas Tremblay. Graph Tikhonov Regularization and Interpolation via Random Spanning Forests. IEEE Transactions on Signal and Information Processing over Networks, 2021. ⟨hal-03012192v1⟩