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On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion.
Scaled Nuclear Norm Minimization for Low-Rank Tensor Completion
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix.
Rank Determination for Low-Rank Data Completion
Moreover, for both single-view matrix and CP tensor, we are able to show that the obtained upper bound is exactly equal to the unknown rank if the lowest-rank completion is given.
Fundamental Conditions for Low-CP-Rank Tensor Completion
Our proposed approach results in characterizing the maximum number of algebraically independent polynomials in terms of a simple geometric structure of the sampling pattern, and therefore we obtain the deterministic necessary and sufficient condition on the sampling pattern for finite completability of the sampled tensor.
Characterization of Deterministic and Probabilistic Sampling Patterns for Finite Completability of Low Tensor-Train Rank Tensor
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i. e., ranks of unfoldings.
Deterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View Data
We provide a deterministic necessary and sufficient condition on the sampling pattern for finite completability.
Deterministic and Probabilistic Conditions for Finite Completability of Low-Tucker-Rank Tensor
We investigate the fundamental conditions on the sampling pattern, i. e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank.
