Matrix Completion With Deterministic Pattern: A Geometric Perspective

@article{Shapiro2019MatrixCW,
  title={Matrix Completion With Deterministic Pattern: A Geometric Perspective},
  author={Alexander Shapiro and Yao Xie and Rui Zhang},
  journal={IEEE Transactions on Signal Processing},
  year={2019},
  volume={67},
  pages={1088-1103}
}
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: Under what conditions will there be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable? We answer the question from a certain point of view and outline a geometric perspective. We give an algebraically verifiable sufficient condition, which we call the well-posedness condition, for the local… Expand
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