The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
An accelerated gradient method for trace norm minimization
Abstract
We consider the minimization of a smooth loss function regularized by the trace norm of the matrix variable. Such formulation finds applications in many machine learning tasks including multi-task learning, matrix classification, and matrix completion. The standard semidefinite programming formulation for this problem is computationally expensive. In addition, due to the non-smooth nature of the trace norm, the optimal first-order black-box method for solving such class of problems converges as O(1/√k), where k is the iteration counter. In this paper, we exploit the special structure of the trace norm, based on which we propose an extended gradient algorithm that converges as O(1/k). We further propose an accelerated gradient algorithm, which achieves the optimal convergence rate of O(1/k2) for smooth problems. Experiments on multi-task learning problems demonstrate the efficiency of the proposed algorithms.
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
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
Bertsekas, D. P. (1997) · Journal of the Operational Research Society · doi:10.1038/sj.jors.2600425 · Cited by 11,726
A Singular Value Thresholding Algorithm for Matrix Completion
Cai, J.-F., Candès, E. J., & Shen, Z. (2010) · SIAM Journal on Optimization · doi:10.1137/080738970 · Cited by 5,809
Introductory Lectures on Convex Optimization: A Basic Course
Nesterov, Y. E. (2014) · Medical Entomology and Zoology · Cited by 3,557
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
Recht, B., Fazel, M., & Parrilo, P. A. (2010) · SIAM Review · doi:10.1137/070697835 · Cited by 3,471
A method for solving the convex programming problem with convergence rate O(1/k^2)
Nesterov, Y. E. (1983) · Доклады Академии наук · Cited by 2,662
Smooth minimization of non-smooth functions
Nesterov, Y. (2005) · Mathematical Programming · doi:10.1007/s10107-004-0552-5 · Cited by 2,455
Advances in Neural Information Processing Systems 18
Murray, I., Mackay, D., Zoubin Ghahramani, A., & Skilling, J. (2006) · Cited by 1,927
Parlar, M. (2000) · Interactive Operations Research with Maple · doi:10.1007/978-1-4612-1356-7_5 · Cited by 1,741
Convex multi-task feature learning
Argyriou, A., Evgeniou, T., & Pontil, M. (2008) · Machine Learning · doi:10.1007/s10994-007-5040-8 · Cited by 1,528
Cited by
Exploiting social relations for sentiment analysis in microblogging
Hu, X., Tang, L., Tang, J., & Liu, H. (2013) · Proceedings of the sixth ACM international conference on Web search and data mining · doi:10.1145/2433396.2433465 · Cited by 384
Metadata
- Authors
- Ji, S., & Ye, J.
- Venue
- Proceedings of the 26th Annual International Conference on Machine Learning
- Publisher
- ACM
- Published
- 2009-06-14
- Pages
- 457-464
- OpenAlex
- W1998635907
- Cited by
- 517
- References
- 30
- FWCI
- 21.39
- Type
- conference paper
- 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: An accelerated gradient method for trace norm minimization. https://app.cochat.ai/papers/10.1145/1553374.1553434
- The paper
- Ji, S., & Ye, J. (2009). An accelerated gradient method for trace norm minimization. Proceedings of the 26th Annual International Conference on Machine Learning. https://doi.org/10.1145/1553374.1553434
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.
