Author:
Ennaji Hamza,Quéau Yvain,Elmoataz Abderrahim
Abstract
AbstractThe aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. We consider a general formulation of Tug-of-War games which is shown to be related to many classical PDEs in the continuous setting. We transcribe these equations on graphs using ad hoc differential operators and we show that it covers several nonlocal PDEs on graphs such as $$\infty $$
∞
-Laplacian, game p-Laplacian and the eikonal equation. This unifying mathematical framework allows us to easily design simple algorithms to solve several inverse problems in imaging and data science, with a particular focus on cultural heritage and medical imaging.
Funder
Agence Nationale de la Recherche
Publisher
Springer Science and Business Media LLC
Reference35 articles.
1. Bertozzi, A. L. & Flenner, A. Diffuse interface models on graphs for classification of high dimensional data. Multiscale Model. Simul. 10, 1090–1118. https://doi.org/10.1137/11083109X (2012).
2. Merkurjev, E., Kostić, T. & Bertozzi, A. L. An MBO scheme on graphs for classification and image processing. SIAM J. Imaging Sci. 6, 1903–1930. https://doi.org/10.1137/120886935 (2013).
3. Garcia-Cardona, C., Merkurjev, E., Bertozzi, A. L., Flenner, A. & Percus, A. G. Multiclass data segmentation using diffuse interface methods on graphs. IEEE Trans. Pattern Anal. Mach. Intell. 36, 1600–1613. https://doi.org/10.1109/TPAMI.2014.2300478 (2014).
4. Mazón, J. M., Solera, M. & Toledo, J. Gradient flows in metric random walk spaces. SeMA J. 79, 3–35. https://doi.org/10.1007/s40324-021-00272-z (2022).
5. Calder, J. & Ettehad, M. Hamilton-jacobi equations on graphs with applications to semi-supervised learning and data depth. J. Mach. Learn. Res. 23, 1–62 (2022).
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献