Research map / Learning theory and algorithms / Matrix and tensor methods
A Sampling-Based Method for Tensor Ring Decomposition
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use leverage-score sampled ALS instead of full TR-ALS | TR decomposition · Pavia Uni., DC Mall, Park Bench, Tabby Cat, and Red Truck (R=10) | Time: up to 1518× speedup | Helped |
| Use leverage-score sampled ALS instead of full TR-ALS | TR decomposition · Pavia Uni., DC Mall, Park Bench, Tabby Cat, and Red Truck (R=10) | Error | Hurt |
| Use leverage-score sampled ALS instead of rTR-ALS | TR decomposition · Real image and video datasets | Time: up to 21× speedup | Helped |
| Use leverage-score sampled ALS instead of TR-ALS | TR decomposition · Highly oscillatory functions: Linear Growth, Airy, and Chirp | Time: 108 ×, 193 × and 17 × | Helped |
| Use leverage-score sampled ALS instead of TR-ALS | TR decomposition · Highly oscillatory functions: Linear Growth, Airy, and Chirp | Error: 0.0102 -> 0.0109; 0.0203 -> 0.0213; 0.0198 -> 0.0210 | No clear effect |
| Replace leverage-score sampling with uniform sampling (ablation) | TR-ALS-Sampled · Pavia Uni., DC Mall, Park Bench, Tabby Cat, and Red Truck (R=10 and R=20) | Error | No clear effect |
| Replace leverage-score sampling with uniform sampling (ablation) | TR-ALS-Sampled · Pavia Uni., DC Mall, Park Bench, Tabby Cat, and Red Truck | Time | No clear effect |
| Replace leverage-score sampling with uniform sampling (ablation) | TR-ALS-Sampled · Real image and video datasets | Samples required: 4.6--8.8 times as many samples | Hurt |
| Use TR-ALS-Sampled features instead of TR-ALS features | k-nearest neighbor classifier (k=1) · COIL-100 classification | Accuracy: 99.07 -> 99.32 | No clear effect |
| Increase the target rank from R=10 to R=20 | TR-ALS-Sampled · Real image and video datasets | Error | Helped |
Closest papers by meaning
- More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees (ICML 2022 · similarity 0.94)
- Efficient Leverage Score Sampling for Tensor Train Decomposition (NeurIPS 2024 · similarity 0.92)
- Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion (AAAI 2019 · similarity 0.91)
- Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery (CVPR 2026 · similarity 0.90)
- Towards Multi-Mode Outlier Robust Tensor Ring Decomposition (AAAI 2024 · similarity 0.88)
- Fast Tensor Completion via Approximate Richardson Iteration (ICML 2025 · similarity 0.88)
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