Research map / Learning theory and algorithms / Matrix and tensor methods
Matrix completion and factorization
Recovers low-rank matrices from partial entries via alternating minimization and sparse regularization.
118 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “matrices · matrix completion · rank matrix”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
21 papers in 2023–24 and 14 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 12.1% to 7.5%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · High-Rank Matrix Completion and Clustering under Self-Expressive Models (NeurIPS 2016 · 44 citations)
- 2017 · Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm (AAAI 2017 · 36 citations)
- 2018 · A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery (ICML 2018 · 22 citations)
- 2019 · Online High Rank Matrix Completion (CVPR 2019 · 41 citations)
- 2020 · Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning (AAAI 2020 · 33 citations)
- 2021 · Unique sparse decomposition of low rank matrices (NeurIPS 2021 · 5 citations)
- 2022 · Undercover Boolean Matrix Factorization with MaxSAT (AAAI 2022 · 3 citations)
- 2023 · Generalization Bounds for Inductive Matrix Completion in Low-Noise Settings (AAAI 2023 · 4 citations)
- 2024 · LERE: Learning-Based Low-Rank Matrix Recovery with Rank Estimation (AAAI 2024 · 5 citations)
- 2025 · Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation (ICLR 2025 · 1 citation)
- 2026 · An Exterior Method for Nonnegative Matrix Factorization (ICML 2026 · 0 citations)
Earliest papers here
- High-Rank Matrix Completion and Clustering under Self-Expressive Models (NeurIPS 2016 · 44 citations)
- Online Low-Rank Subspace Clustering by Basis Dictionary Pursuit (ICML 2016 · 42 citations)
- Dictionary Learning for Massive Matrix Factorization (ICML 2016 · 37 citations)
What has been tried
101 papers here report 776 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 12%, hurt 16%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| universally simplify the matrix before factorization | Synthetic BMF, rank 20, densities 0.1–0.4 · computation time | 5m -> 4s; 14m -> 4s; 20m -> 3s; 30m -> 2s | Helped | Delegation-Relegation for Boolean Matrix Factorization (AAAI 2024 · 1 citation) |
| use weighted-norm regularization | Douban test · RMSE | 0.7627 -> 0.7626 | Helped | Generalization Analysis of Deep Non-linear Matrix Completion (ICML 2024) |
| decrease initialization scale | Connected matrix completion, target with one unknown element · rank | Helped | Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion (NeurIPS 2024) |
What reviewers will expect
Datasets and baselines named in the 10 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MovieLens-100k · 2 of 10 papers
Baselines
- Maxide · 2 of 10 papers
- DirtyIMC · 2 of 10 papers
- FNNM · 2 of 10 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 35 papers; from OpenAlex and the papers' affiliations).
- Google · 4 papers
- University of California, Berkeley · 3 papers
- Singapore Management University · 2 papers
- Czech Technical University in Prague · 2 papers
- University of Wisconsin - Madison · 2 papers
- Shanghai Jiao Tong University · 2 papers
- Carnegie Mellon University · 2 papers
- Massachusetts Institute of Technology · 2 papers
- University of Texas at Austin · 2 papers
- Microsoft · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Low-rank approximation theory (142 papers)
- Randomized sketching for matrices (96 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 papers)
Elsewhere in the topic
- Nonconvex low-rank and sparse optimization (112 papers)
- Sparse regression with guarantees (94 papers)
- High-dimensional estimation theory (89 papers)
- Signal recovery and phase retrieval (66 papers)
- Sparse and robust PCA (66 papers)
- Tensor network decompositions (45 papers)
- Low-rank tensor completion (45 papers)
- Randomized tensor decomposition algorithms (43 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).