Research map / Learning theory and algorithms / Matrix and tensor methods
A Subspace Learning Approach for High Dimensional Matrix Decomposition with Efficient Column/Row Sampling
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 |
|---|---|---|---|
| Informative (leverage-based) column/row sampling instead of uniform sampling (ablation) | Proposed decomposition on clustered/structured low-rank data · 2000x4200 clustered LR matrix, rank 60 | number of samples needed for correct decomposition: significantly smaller number of samples required than uniform sampling | Helped |
| Uniform random sampling of columns/rows with m1=m2=10r | Proposed Algorithm 1 · Synthetic N1=N2 from 500 to 2x10^4, rank 5, rho=0.02 | speedup over full decomposition (2): 90x to 4800x speedup | Helped |
| Increasing rank r with uniform sampling (phase transition) | Proposed Algorithm 1 · 1000x1000 matrix, Bernoulli rho=0.02 | required number of sampled columns/rows: required samples increase with rank | Hurt |
| Increasing data matrix size with fixed rank under uniform sampling | Proposed Algorithm 1 · Phase transition, varying N1=N2 with fixed rank | required number of sampled columns/rows: almost independent of data size | No clear effect |
| Alternating column/row sampling (Algorithm 3) on highly structured LR matrix (ablation) | Column sampling for 10250x10250 matrix, n=100 clusters · Rank of sampled columns over iterations | rank of Dc after iterations: converges to rank of L in less than 3 iterations | Helped |
| Using uniform sampling of columns for clustered data as cluster count grows | Column sampling for clustered LR matrix · 2000x6150 clustered matrix, rank 60 | number of uniformly sampled columns needed to span CS: more than half of columns needed at n=60 clusters | Hurt |
| Using 500 randomly sampled rows for representation learning in background subtraction | Proposed approach on lobby video · Background subtraction video | running time: few milliseconds vs about half an hour for (2) | Helped |
Closest papers by meaning
- High-Dimensional Optimization in Adaptive Random Subspaces (NeurIPS 2019 · similarity 0.89)
- Learning-Based Low-Rank Approximations (NeurIPS 2019 · similarity 0.88)
- A Kernel Random Matrix-Based Approach for Sparse PCA (ICLR 2019 · similarity 0.87)
- Subspace Clustering With Priors via Sparse Quadratically Constrained Quadratic Programming (CVPR 2016 · similarity 0.87)
- High Rank Matrix Completion With Side Information (AAAI 2018 · similarity 0.87)
- Multi-Subspace Matrix Recovery from Permuted Data (AAAI 2025 · similarity 0.86)
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.