Characterization Of sampling patterns for low-tt-rank tensor retrieval

• Published in: Annals of mathematics and artificial intelligence Vol. 88; no. 8; pp. 859 - 886
• Main Authors: Ashraphijuo, Morteza, Wang, Xiaodong
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2020; Springer; Springer Nature B.V
• Subjects: Algebra; Artificial Intelligence; Complex Systems; Computer Science; Decomposition; Lower bounds; Manifolds (mathematics); Mathematical analysis; Mathematics; Polynomials; Sampling; Statistical analysis; Tensors; Tensor-train decomposition; Finite completability; 68W01; Data completion; Tensor retrieval; Low-rank tensor completion; Unique completability

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 TT unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the location...