Research map / Learning theory and algorithms / Matrix and tensor methods
A Nonconvex Projection Method for Robust PCA
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use nonconvex set feasibility with alternating projections instead of RPCA objective-based algorithms | RPCA · Synthetic RPCA | recovery success: approximately up to 63% versus 50% | Helped |
| Use feasibility projections rather than RPCA algorithms | RPCA · Synthetic RPCA with low sparsity | recovery success: ρ_r≤0.4 | Helped |
| Use the feasibility method rather than RPCA GD | RMC · Synthetic RMC with decreasing observed-entry fraction | recovery success | Helped |
| Use RPCA GD rather than the feasibility method | RMC · Synthetic RMC with 50% and 75% observed entries as rank increases | RMSE | Helped |
| Use the feasibility method rather than RPCA GD | RMC · Synthetic RMC with fewer observed entries | RMSE | Helped |
| Use the feasibility method rather than RPCA GD | RMC background and foreground estimation · Basic sequence, Stuttgart dataset | foreground pixel proximity: more than 95% | Helped |
| Underestimate the target rank or sparsity level (ablation) | Alternating projection RPCA · Synthetic RPCA | convergence | Hurt |
| Overestimate the target rank or sparsity level (ablation) | Alternating projection RPCA · Synthetic RPCA | convergence speed | Hurt |
| Use a medium fraction of observed entries instead of a small or large fraction (ablation) | Alternating projection RMC · Synthetic RMC | convergence: ≈0.5(m·n) | Hurt |
| Use small true rank and sparsity levels (ablation) | Alternating projection RPCA · Synthetic RPCA | convergence speed: 10% or less; 15% or less | Helped |
Closest papers by meaning
- Fast and Provable Nonconvex Tensor RPCA (ICML 2022 · similarity 0.91)
- RES-PCA: A Scalable Approach to Recovering Low-Rank Matrices (CVPR 2019 · similarity 0.89)
- Informed Non-Convex Robust Principal Component Analysis With Features (AAAI 2018 · similarity 0.88)
- Efficient Robust Principal Component Analysis via Block Krylov Iteration and CUR Decomposition (CVPR 2023 · similarity 0.87)
- Efficient Sparse PCA via Block-Diagonalization (ICLR 2025 · similarity 0.85)
- Rethinking PCA Through Duality (NeurIPS 2025 · similarity 0.85)
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