Research map / Learning theory and algorithms / Matrix and tensor methods
Sparse and robust PCA
Designs provable algorithms for sparse PCA and subspace recovery under noise, missing data and outliers.
66 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “sparse · recovery · pca”
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.
7 papers in 2023–24 and 9 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.0% to 4.8%.
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 · Dimensionality Reduction of Massive Sparse Datasets Using Coresets (NeurIPS 2016 · 34 citations)
- 2017 · Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis (ICML 2017 · 27 citations)
- 2018 · Robust Formulation for PCA: Avoiding Mean Calculation With L2,p-norm Maximization (AAAI 2018 · 17 citations)
- 2019 · On Robustness of Principal Component Regression (NeurIPS 2019 · 22 citations)
- 2020 · Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing (NeurIPS 2020 · 12 citations)
- 2021 · Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection (NeurIPS 2021 · 19 citations)
- 2022 · Generative Principal Component Analysis (ICLR 2022 · 6 citations)
- 2023 · Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA (ICML 2023 · 0 citations)
- 2024 · Fun with Flags: Robust Principal Directions via Flag Manifolds (CVPR 2024 · 3 citations)
- 2025 · Rethinking PCA Through Duality (NeurIPS 2025 · 0 citations)
- 2026 · Mean-Shift PCA by Knockoff Mean (ICML 2026 · 0 citations)
Earliest papers here
- Dimensionality Reduction of Massive Sparse Datasets Using Coresets (NeurIPS 2016 · 34 citations)
- Robust Principal Component Analysis with Side Information (ICML 2016 · 33 citations)
- An Efficient Exact-PGA Algorithm for Constant Curvature Manifolds (CVPR 2016 · 13 citations)
What has been tried
55 papers here report 361 measured changes (a component added, removed or swapped, compared with a baseline): helped 66%, no clear effect 9%, hurt 19%, 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 |
|---|---|---|---|---|
| Replace the direct spectral algorithm with a nonlinear Laplacian using a Z-shaped nonlinearity | Gaussian Planted Submatrix · critical signal strength β* | 1 -> \num{0.765} | Helped | Nonlinear Laplacians: Tunable principal component analysis under directional prior information (NeurIPS 2025 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 16 papers; from OpenAlex and the papers' affiliations).
- KU Leuven · 2 papers
Use it
Download BibTeX of 34 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Sparse regression with guarantees (94 papers)
- High-dimensional estimation theory (89 papers)
- Signal recovery and phase retrieval (66 papers)
- Nonconvex low-rank and sparse optimization (112 papers)
Elsewhere in the topic
- Low-rank approximation theory (142 papers)
- Matrix completion and factorization (118 papers)
- Randomized sketching for matrices (96 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 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).