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- W4385507606 abstract "Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a emph{Trust-Region Subproblem} (TRS). This reformulation is motivated by the well-posedness of Laplacian eigenvectors in the limit of infinite unlabeled data. To solve this problem, we first show that a first-order condition implies the solution of a manifold alignment problem and that solutions to the classical emph{Orthogonal Procrustes} problem can be used to efficiently find good classifiers that are amenable to further refinement. Next, we address the criticality of selecting supervised samples at low-label rates. We characterize informative samples with a novel measure of centrality derived from the principal eigenvectors of a certain submatrix of the graph Laplacian. We demonstrate that our framework achieves lower classification error compared to recent state-of-the-art and classical semi-supervised learning methods at extremely low, medium, and high label rates. Our code is available on githubfootnote{anonymized for submission}." @default.
- W4385507606 created "2023-08-03" @default.
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- W4385507606 date "2023-07-31" @default.
- W4385507606 modified "2023-09-23" @default.
- W4385507606 title "Semi-Supervised Laplacian Learning on Stiefel Manifolds" @default.
- W4385507606 doi "https://doi.org/10.48550/arxiv.2308.00142" @default.
- W4385507606 hasPublicationYear "2023" @default.
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