Research map / Learning theory and algorithms / Matrix and tensor methods
Algorithms for $\ell_p$ Low-Rank Approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use entrywise ℓ1 optimization instead of the SVD objective | Algorithm 2 on FIDAP · FIDAP matrix | ℓ1 error: roughly 40% | Helped |
| Use entrywise ℓ∞ optimization instead of the SVD objective | Algorithm 2 on KOS · KOS blog entries matrix | ℓ∞ error: around 10% | Helped |
| Use entrywise ℓ1 optimization instead of the SVD objective | Algorithm 2 on the random matrix · Random matrix | ℓ1 error | Helped |
| Use entrywise ℓ∞ optimization instead of the SVD objective | Algorithm 2 on the random matrix · Random matrix | ℓ∞ error: around 10% | Helped |
| Use entrywise ℓ1 optimization instead of the SVD objective | Algorithm 2 on the random ±1 matrix · Random ±1 matrix | ℓ1 error: between 30% and 50% | Helped |
| Use entrywise ℓ∞ optimization instead of the SVD objective | Algorithm 2 on the random ±1 matrix · Random ±1 matrix | ℓ∞ error: between 30% and 50% | Helped |
| Use adaptive uniform sampling and iterative covering to select columns | Algorithm 3 · k-CSS_p, p ∈ [1, ∞] | approximation factor: O(k) | Helped |
| Reduce the bicriteria rank to exactly k using an almost-ℓp-isoperimetric transformation | Algorithm 4 · k-LRA_p | approximation factor: O((k4 log k)δ) | Helped |
| Use the polynomial-time rank-reduction variant rather than the lower-approximation-factor rank-reduction algorithm | Rank-reduction algorithm · k-LRA_p, constant p ≥ 1 | approximation factor: (k log m)O(p)δ | Mixed |
Closest papers by meaning
- Approximation Algorithms for $\ell_0$-Low Rank Approximation (NeurIPS 2017 · similarity 0.94)
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- Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation (ICLR 2025 · similarity 0.87)
- Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time (ICLR 2024 · similarity 0.86)
- Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacy (NeurIPS 2025 · similarity 0.86)
- Reweighted Solutions for Weighted Low Rank Approximation (ICML 2024 · similarity 0.85)
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