Semi-Supervised Laplace Learning on Stiefel Manifolds
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916356776001536 |
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| author | Holtz, Chester Chen, Pengwen Cloninger, Alexander Cheng, Chung-Kuan Mishne, Gal |
| author_facet | Holtz, Chester Chen, Pengwen Cloninger, Alexander Cheng, Chung-Kuan Mishne, Gal |
| contents | 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. To tackle refinement, we develop the framework of Sequential Subspace Optimization for graph-based SSL. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00142 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-Supervised Laplace Learning on Stiefel Manifolds Holtz, Chester Chen, Pengwen Cloninger, Alexander Cheng, Chung-Kuan Mishne, Gal Machine Learning 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. To tackle refinement, we develop the framework of Sequential Subspace Optimization for graph-based SSL. 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. |
| title | Semi-Supervised Laplace Learning on Stiefel Manifolds |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2308.00142 |