The Algebraic Combinatorial Approach for Low-Rank Matrix Completion

  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},
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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