Note: low-rank tensor train completion with side information based on Riemannian optimization

2020/06/23 by Stanislav Budzinskiy, Budzinskiy, Stanislav, Н. Л. Замарашкин +2 · 4 citations
Computer Science · Engineering · Mathematics · #Algebra over a field #Algorithm #Blind Source Separation Techniques #Combinatorics #Computer science #Exact solutions in general relativity #FOS: Mathematics #Linear subspace #Mathematical analysis #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Pure mathematics #Rank (graph theory) #Sparse and Compressive Sensing Techniques #Symmetric tensor #Tensor (intrinsic definition) #Tensor decomposition and applications #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2006.12798

published in arXiv (Cornell University) (Cornell University)

arxiv created 2020/06/23 · openalex publication_date 2020/06/23 · arxiv updated 2020/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We consider the low-rank tensor train completion problem when additional side information is available in the form of subspaces that contain the mode-k fiber spans. We propose an algorithm based on Riemannian optimization to solve the problem. Numerical experiments show that the proposed algorithm requires far fewer known entries to recover the tensor compared to standard tensor train completion methods.

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