Matrix Completion From a Few Entries

@article{Keshavan2010MatrixCF,
  title={Matrix Completion From a Few Entries},
  author={Raghunandan H. Keshavan and A. Montanari and Sewoong Oh},
  journal={IEEE Transactions on Information Theory},
  year={2010},
  volume={56},
  pages={2980-2998}
}
  • Raghunandan H. Keshavan, A. Montanari, Sewoong Oh
  • Published 2010
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • Let M be an n¿ × n matrix of rank r, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm, which we call OptSpace, that reconstructs M from |E| = O(rn) observed entries with relative root mean square error 1/2 RMSE ¿ C(¿) (nr/|E|)1/2 with probability larger than 1 - 1/n3. Further, if r = O(1) and M is sufficiently unstructured, then OptSpace reconstructs it exactly from |E| = O(n log n) entries with probability larger than 1 - 1/n3. This… CONTINUE READING
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