Analysis and algorithms for ℓ-based semi-supervised learning on graphs
نویسندگان
چکیده
This paper addresses theory and applications of ℓ p -based Laplacian regularization in semi-supervised learning. The graph -Laplacian for > 2 has been proposed recently as a replacement the standard ( = ) learning problems with very few labels, where is degenerate. In first part we prove new discrete to continuum convergence results -Laplace on k -nearest neighbor -NN) graphs, which are more commonly used practice than random geometric graphs. Our analysis shows that, -NN retains information about data distribution → ∞ Lipschitz sensitive distribution. situation can be contrasted forgets . We also present general framework proving graph-based that only requires pointwise consistency monotonicity. second paper, develop fast algorithms solving variational game-theoretic equations weighted graphs several efficient scalable both formulations, numerical synthetic indicating their properties. Finally, conduct extensive experiments MNIST, FashionMNIST EMNIST datasets illustrate effectiveness formulation labels. particular, find performs well labels experimentally validates our theoretical findings (the unlabeled data)
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2022
ISSN: ['1096-603X', '1063-5203']
DOI: https://doi.org/10.1016/j.acha.2022.01.004