Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provably

@inproceedings{Park2016FindingLS,
  title={Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provably},
  author={Dohyung Park and Anastasios Kyrillidis and Constantine Caramanis and Sujay Sanghavi},
  year={2016}
}
A rank-r matrix X ∈ Rm×n can be written as a product UV >, where U ∈ Rm×r and V ∈ Rn×r. One could exploit this observation in optimization: e.g., consider the minimization of a convex function f(X) over rank-r matrices, where the set of rank-r matrices is modeled via the factorization UV >. Though such parameterization reduces the number of variables, and is more computationally efficient (of particular interest is the case r min{m,n}), it comes at a cost: f(UV >) becomes a non-convex function… CONTINUE READING
Highly Cited
This paper has 18 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 11 extracted citations

Ranking from Crowdsourced Pairwise Comparisons via Smoothed Matrix Manifold Optimization

2017 IEEE International Conference on Data Mining Workshops (ICDMW) • 2017
View 10 Excerpts
Highly Influenced

Symmetry. Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization

2018 Information Theory and Applications Workshop (ITA) • 2018
View 1 Excerpt

Robust Kronecker-Decomposable Component Analysis for Low-Rank Modeling

2017 IEEE International Conference on Computer Vision (ICCV) • 2017
View 1 Excerpt

Finding low-rank solutions to smooth convex problems via the Burer-Monteiro approach

2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton) • 2016
View 7 Excerpts

References

Publications referenced by this paper.
Showing 1-10 of 108 references

E

M. Davenport, Y. Plan
van den Berg, and M. Wootters. 1-bit matrix completion. Information and Inference, 3(3):189–223 • 2014
View 9 Excerpts
Highly Influenced

Guaranteed Matrix Completion via Non-Convex Factorization

IEEE Transactions on Information Theory • 2015
View 8 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…