# Semi-Supervised Laplace Learning on Stiefel Manifolds

arXiv: https://arxiv.org/abs/2308.00142 · HTML: https://mlsanity.com/paper/2308.00142/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 57 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Analysis and algorithms for ℓp-based semi-supervised learning on graphs](https://mlsanity.com/paper/1901.05031/) (2019)
- [Active Learning on Trees and Graphs](https://mlsanity.com/paper/1301.5112/) (2013)

## Built on by (most cited first, 1 of 1)

- [Graph-based Semi-Supervised Learning via Maximum Discrimination](https://mlsanity.com/paper/2602.08042/) (2026)

## Abstract (arXiv)

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 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 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.