Iterative hard thresholding for low CP-rank tensor models. Issue 22 (21st December 2022)

• Record Type: Journal Article
• Authors: Grotheer, R.; Li, S.; Ma, A.; Needell, D.; Qin, J.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 22(2022)
• Page Start: 7452
• Page End: 7468
• Publication Date: 2022-12-21
• Subjects: Iterative hard thresholding -- tensors -- CP rank -- restricted isometry property -- low-rank tensor recovery; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1992335
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, extensions to tensor recovery have only recently began to be studied and developed, despite an abundance of practical tensor applications. Recently, a tensor variant of the Iterative Hard Thresholding method was proposed and theoretical results were obtained that exact guarantee recovery of tensors with low Tucker rank. In this paper, we utilize and prove a similar tensor version of the Restricted Isometry Property (RIP) to extend these results for tensors with low CANDECOMP/PARAFAC (CP) rank. In doing so, we leverage recent results on efficient approximations of CP decompositions that remove the need for challenging assumptions in prior works. We complement our theoretical findings with empirical results that showcase the potential of the approach.