Abstract
We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data. In particular, we show that the continuum limit of graph-based semi-supervised learning with the game theoretic p-Laplacian is a weighted version of the continuous p-Laplace equation. We also prove that solutions to the graph p-Laplace equation are approximately Hölder continuous with high probability. Our proof uses the viscosity solution machinery and the maximum principle on a graph.
Original language | English (US) |
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Pages (from-to) | 301-330 |
Number of pages | 30 |
Journal | Nonlinearity |
Volume | 32 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2019 |
Bibliographical note
Funding Information:The author gratefully acknowledges the support of NSF-DMS grant 1713691. The author is also grateful to the anonymous referees, whose suggestions have greatly improved the paper.
Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society.
Keywords
- consistency
- continuum limit
- game theoretic p-Laplacian
- maximum principle
- probability
- semi-supervised learning
- viscosity solutions