Research map / Learning theory and algorithms / Matrix and tensor methods
Approximation Algorithms for $\ell_0$-Low Rank Approximation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Allow output rank O(k log(n/k)) and use recursive random column selection | Reals ℓ0 rank-k approximation · Reals ℓ0 rank-k | approximation factor: O(k^2 log(n/k)) | Helped |
| Use sampled columns and sampled cost estimates instead of scanning all nonzero entries | Reals ℓ0 rank-1 approximation · Reals ℓ0 rank-1 | running time: O\left(\Big( \frac{n\log m}{\epsilon^{2}}+ \min\Big\{\nnz{A},\ n+\psi^{-1}\frac{\log n}{\epsilon^{2}}\Big\}\Big) \frac{\ | Helped |
| Use a binary-factor algorithm tuned to small ψ | Boolean ℓ0 rank-1 approximation · Boolean ℓ0 rank-1 | approximation factor: (1+500\psi) | Helped |
| Use row and column sums as input to avoid computing them from the matrix | Boolean ℓ0 rank-1 algorithm for known φ · Boolean ℓ0 rank-1 with OPT/nnz(A) ≤ φ | running time: O(\nnz{A} + m+n) -> O(m+n) | Helped |
| Restrict attention to a column-based rank-1 approximation | Reals ℓ0 rank-1 approximation · Reals ℓ0 rank-1 | approximation factor: 2(1-1/n) | Hurt |
| Require the approximation to use k columns selected from the input | Reals ℓ0 rank-k approximation · Reals ℓ0 rank-k | approximation factor: \Omega(k) | Hurt |
Closest papers by meaning
- Algorithms for $\ell_p$ Low-Rank Approximation (ICML 2017 · similarity 0.94)
- Consistent Low-Rank Approximation (ICLR 2026 · similarity 0.92)
- Additive Error Guarantees for Weighted Low Rank Approximation (ICML 2021 · similarity 0.91)
- Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation (ICLR 2025 · similarity 0.89)
- Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time (ICLR 2024 · similarity 0.88)
- Entrywise error bounds for low-rank approximations of kernel matrices (NeurIPS 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.