The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Exact matrix completion via convex optimization
Abstract
Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem that finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., & Tygert, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709640104 · Cited by 559
Cited by
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2693418 · Cited by 3,661
Tensor Completion for Estimating Missing Values in Visual Data
Liu, J., Musialski, P., Wonka, P., & Ye, J. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.39 · Cited by 2,063
The Power of Convex Relaxation: Near-Optimal Matrix Completion
Candes, E. J., & Tao, T. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2044061 · Cited by 2,060
Recovering Gene Interactions from Single-Cell Data Using Data Diffusion
van Dijk, D., Sharma, R., Nainys, J., Yim, K., Kathail, P., Carr, A. J., Burdziak, C., Moon, K. R., Chaffer, C. L., Pattabiraman, D., et al. (2018) · Cell · doi:10.1016/j.cell.2018.05.061 · Cited by 1,829
CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters
Levie, R., Monti, F., Bresson, X., & Bronstein, M. M. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2018.2879624 · Cited by 685
Metadata
- Authors
- Candès, E., & Recht, B.
- Venue
- Communications of the ACM
- Published
- 2012-06
- Volume
- 55
- Issue
- 6
- Pages
- 111-119
- ISSN
- 0001-0782 (ISSN-L)
- 1557-7317
- OpenAlex
- W2124608575
- Cited by
- 996
- References
- 1
- FWCI
- 71.17
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Exact matrix completion via convex optimization. https://app.cochat.ai/papers/10.1145/2184319.2184343
- The paper
- Candès, E., & Recht, B. (2012). Exact matrix completion via convex optimization. Communications of the ACM. https://doi.org/10.1145/2184319.2184343
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
