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Low-rank tensor completion: a Riemannian manifold preconditioning approach
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed Tucker-manifold metric instead of the Euclidean metric (ablation) | Riemannian gradient descent · Synthetic tensor, size 200 × 200 × 200, rank (10,10,10), OS = 10 | training error | Helped |
| Use the proposed batch conjugate-gradient method instead of geomCG | Tensor completion · Ribeira, OS = 11 | test MSE: 8.2095\cdot 10^{-4} \pm 1.7\cdot 10^{-5} vs 3.8342 \cdot 10^{-1} \pm 4.2 \cdot 10^{-2} | Helped |
| Use the proposed batch conjugate-gradient method instead of geomCG | Tensor completion · MovieLens-10M, rank (10,10,10) | test MSE: 1.0107 \pm 2.7 \cdot 10^{-2} vs 1.6550 \pm 8.7 \cdot 10^{-2} | Helped |
| Use the proposed batch algorithm instead of geomCG | Large-scale synthetic tensor completion · Large-scale instances | convergence | Helped |
| Use the proposed batch algorithm instead of geomCG | Tensor completion with sparse observations · Case S4, OS = 4 | test error | Helped |
| Use the proposed batch algorithm instead of geomCG | Tensor completion with noisy observations · Case S6, noise levels ε = {10^-4, 10^-6, 10^-8, 10^-10, 10^-12} | convergence speed | Helped |
| Use the proposed online stochastic-gradient method instead of TeCPSGD or OLSTEC | Online tensor completion · Airport Hall surveillance video | test MSE | Helped |
| Use the proposed online stochastic-gradient method instead of its batch counterpart | Online tensor completion · Synthetic tensor, size 100 × 100 × 10000 | asymptotic test MSE | No clear effect |
Closest papers by meaning
- Preconditioned Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Completion (ICML 2025 · similarity 0.94)
- Convergence and Complexity Guarantee for Inexact First-order Riemannian Optimization Algorithms (ICML 2024 · similarity 0.89)
- Fast Tensor Completion via Approximate Richardson Iteration (ICML 2025 · similarity 0.88)
- Riemannian coordinate descent algorithms on matrix manifolds (ICML 2024 · similarity 0.87)
- Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method (ICML 2025 · similarity 0.87)
- Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space (NeurIPS 2025 · similarity 0.86)
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