Algorithms for ℓ_p-based semi-supervised learning on graphs
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We develop fast algorithms for solving the variational and game-theoretic p-Laplace equations on weighted graphs for p>2. The graph p-Laplacian for p>2 has been proposed recently as a replacement for the standard (p=2) graph Laplacian in semi-supervised learning problems with very few labels, where the minimizer of the graph Laplacian becomes degenerate. We present several efficient and scalable algorithms for both the variational and game-theoretic formulations, and present numerical results on synthetic data and on classification and regression problems that illustrate the effectiveness of the p-Laplacian for semi-supervised learning with few labels.
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