The Algebraic Combinatorial Approach for Low-Rank Matrix Completion

@article{Kirly2015TheAC,
  title={The Algebraic Combinatorial Approach for Low-Rank Matrix Completion},
  author={Franz J. Kir{\'a}ly and Louis Theran and Ryota Tomioka and Takeaki Uno},
  journal={Journal of Machine Learning Research},
  year={2015},
  volume={16},
  pages={1391-1436}
}
We propose an algebraic combinatorial framework for the problem of completing partially observed low-rank matrices. We show that the intrinsic properties of the problem, including which entries can be reconstructed, and the degrees of freedom in the reconstruction, do not depend on the values of the observed entries, but only on their position. We associate combinatorial and algebraic objects, differentials and matroids, which are descriptors of the particular reconstruction task, to the set of… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 48 references

Matroid theory, volume 21 of Oxford Graduate Texts in Mathematics

  • James Oxley
  • 2011
Highly Influential
4 Excerpts

The Red Book of Varieties and Schemes

  • David Mumford
  • Lecture Notes in Mathematics. Springer-Verlag…
  • 1999
Highly Influential
6 Excerpts

Edge-disjoint spanning trees of finite graphs

  • C. St. J.A. Nash-Williams
  • J. London Math. Soc.,
  • 1961
Highly Influential
2 Excerpts

On the problem of decomposing a graph into n connected factors

  • William T. Tutte
  • J. London Math. Soc.,
  • 1961
Highly Influential
2 Excerpts

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