Research map / Learning theory and algorithms / Matrix and tensor methods
Low-rank tensor completion
Recovers missing tensor entries with nuclear norm, nonconvex and approximate iterative methods.
45 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “tensors · decomposition · rank tensor”
State History Tried 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.
6 papers in 2023–24 and 8 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 3.5% to 4.3%.
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 · Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (CVPR 2016 · 556 citations)
- 2017 · Low-Rank Tensor Completion with Total Variation for Visual Data Inpainting (AAAI 2017 · 131 citations)
- 2018 · Missing Slice Recovery for Tensors Using a Low-Rank Model in Embedded Space (CVPR 2018 · 117 citations)
- 2019 · Non-Local Meets Global: An Integrated Paradigm for Hyperspectral Denoising (CVPR 2019 · 194 citations)
- 2020 · Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction (AAAI 2020 · 51 citations)
- 2021 · Beyond the Signs: Nonparametric Tensor Completion via Sign Series (NeurIPS 2021 · 2 citations)
- 2022 · Multi-Mode Tensor Space Clustering Based on Low-Tensor-Rank Representation (AAAI 2022 · 6 citations)
- 2023 · Enhanced Tensor Low-Rank and Sparse Representation Recovery for Incomplete Multi-View Clustering (AAAI 2023 · 81 citations)
- 2024 · Towards Multi-Mode Outlier Robust Tensor Ring Decomposition (AAAI 2024 · 9 citations)
- 2025 · OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems (AAAI 2025 · 3 citations)
- 2026 · Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery (CVPR 2026 · 0 citations)
Earliest papers here
- Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization (CVPR 2016 · 556 citations)
- Low-Rank Regression with Tensor Responses (NeurIPS 2016 · 48 citations)
- Robust Tensor Factorization With Unknown Noise (CVPR 2016 · 38 citations)
What has been tried
38 papers here report 274 measured changes (a component added, removed or swapped, compared with a baseline): helped 71%, no clear effect 8%, hurt 14%, mixed 8%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| add OTV loss | CAVE tensor completion, Balloons, SR=0.05 · PSNR | 37.64 -> 40.20 | Helped | OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems (AAAI 2025 · 3 citations) |
| Use accelerated-mini-ALS instead of mini-ALS | Cardiac-MRI and hyperspectral · solution quality | Helped | Fast Tensor Completion via Approximate Richardson Iteration (ICML 2025 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 14 papers; from OpenAlex and the papers' affiliations).
- Xi’an Jiaotong University · 2 papers
Use it
Download BibTeX of 31 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Tensor network decompositions (45 papers)
- Randomized tensor decomposition algorithms (43 papers)
Elsewhere in the topic
- Low-rank approximation theory (142 papers)
- Matrix completion and factorization (118 papers)
- Nonconvex low-rank and sparse optimization (112 papers)
- Randomized sketching for matrices (96 papers)
- Sparse regression with guarantees (94 papers)
- High-dimensional estimation theory (89 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 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).