Guaranteed Matrix Completion via Nonconvex Factorization

@article{Sun2015GuaranteedMC,
  title={Guaranteed Matrix Completion via Nonconvex Factorization},
  author={Ruoyu Sun and Z. Luo},
  journal={2015 IEEE 56th Annual Symposium on Foundations of Computer Science},
  year={2015},
  pages={270-289}
}
  • Ruoyu Sun, Z. Luo
  • Published 2015
  • Computer Science
  • 2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • Matrix factorization is a popular approach for large-scale matrix completion. In this approach, the unknown low-rank matrix is expressed as the product of two much smaller matrices so that the low-rank property is automatically fulfilled. The resulting optimization problem, even with huge size, can be solved (to stationary points) very efficiently through standard optimization algorithms such as alternating minimization and stochastic gradient descent (SGD). However, due to the non-convexity… CONTINUE READING
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    References

    SHOWING 1-10 OF 68 REFERENCES
    Guaranteed Matrix Completion via Nonconvex Factorization
    • 22
    On the Provable Convergence of Alternating Minimization for Matrix Completion
    • 25
    • PDF
    Understanding Alternating Minimization for Matrix Completion
    • M. Hardt
    • Computer Science, Mathematics
    • 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
    • 2014
    • 195
    • PDF
    Low-rank matrix completion using alternating minimization
    • 751
    • Highly Influential
    • PDF
    Universal Matrix Completion
    • 78
    • PDF
    Fast Exact Matrix Completion with Finite Samples
    • 69
    • PDF
    Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
    • 565
    • PDF
    The Power of Convex Relaxation: Near-Optimal Matrix Completion
    • E. Candès, T. Tao
    • Mathematics, Computer Science
    • IEEE Transactions on Information Theory
    • 2010
    • 1,680
    • PDF
    Fixed point and Bregman iterative methods for matrix rank minimization
    • 891
    • PDF
    Coherent Matrix Completion
    • 96
    • PDF