no code implementations • 5 Dec 2017 • Morteza Ashraphijuo, Vaneet Aggarwal, Xiaodong Wang
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.
no code implementations • 25 Jul 2017 • Morteza Ashraphijuo, Xiaodong Wang
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix.
no code implementations • 3 Jul 2017 • Morteza Ashraphijuo, Xiaodong Wang, Vaneet Aggarwal
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.
no code implementations • 31 Mar 2017 • Morteza Ashraphijuo, Xiaodong Wang
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.
no code implementations • 22 Mar 2017 • Morteza Ashraphijuo, Xiaodong Wang
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.
no code implementations • 3 Jan 2017 • Morteza Ashraphijuo, Xiaodong Wang, Vaneet Aggarwal
We provide a deterministic necessary and sufficient condition on the sampling pattern for finite completability.
no code implementations • 6 Dec 2016 • Morteza Ashraphijuo, Vaneet Aggarwal, Xiaodong Wang
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.