最近在看Matrix Completion相關的文章，本來想自己總結一下，看到這裏總結的不錯就轉載過來了。
http://www.svt.caltech.edu/
MATRIX COMPLETION PAPERS
We distinguish two types of matrix completion: matrix completion when a subset of entries is observed, and matrix completion when a linear functional of the entire matrix is observed. SVT, and the papers below, deal with the first type; for an introduction to the latter type (which is in some sense an extension of compressed sensing), Guaranteed minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , by Recht, Fazel and Parrilo, is a good place to start.
Theory:
- Exact matrix completion via convex optimization by E. J. Candès and B. Recht (2008).
- Necessary and Sufficient Condtions for Success of the Nuclear Norm Heuristic for Rank Minimization , by B. Recht, W. Xu and B. Hassibi (2008). The extended technical report has full proofs.
- The power of convex relaxation: Near-optimal matrix completion , by E. Candès and T. Tao (2009).
- Matrix completion with noise , by E. J. Candès and Y. Plan (2009).
Algorithms:
- A singular value thresholding algorithm for matrix completion by J-F. Cai, E. J. Candès and Z. Shen (2008).
- Fixed point and Bregman iterative methods for matrix rank minimization by S. Ma, D. Goldfarb and L. Chen (2008).
- Interior-point method for nuclear norm approximation with application to system identification by Z. Lui and L. Vandenberghe (2008).
- Matrix Completion from a Few Entries , by R. Keshavan, A. Montanari, and S. Oh (2009).
- An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems by K. Toh and S. Yun (2009).