Robust low-tubal-rank tensor completion via convex optimization

Qiang Jiang, Kwok Po NG*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

12 Citations (Scopus)

Abstract

This paper considers the problem of recovering multidimensional array, in particular third-order tensor, from a random subset of its arbitrarily corrupted entries. Our study is based on a recently proposed algebraic framework in which the tensor-SVD is introduced to capture the low-tubal-rank structure in tensor. We analyze the performance of a convex program, which minimizes a weighted combination of the tensor nuclear norm, a convex surrogate for the tensor tubal rank, and the tensor `1 norm. We prove that under certain incoherence conditions, this program can recover the tensor exactly with overwhelming probability, provided that its tubal rank is not too large and that the corruptions are reasonably sparse. The number of required observations is order optimal (up to a logarithm factor) when comparing with the degrees of freedom of the low-tubal-rank tensor. Numerical experiments verify our theoretical results and real-world applications demonstrate the effectiveness of our algorithm.

Original languageEnglish
Title of host publicationProceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
EditorsSarit Kraus
PublisherInternational Joint Conferences on Artificial Intelligence
Pages2649-2655
Number of pages7
ISBN (Electronic)9780999241141
DOIs
Publication statusPublished - 2019
Event28th International Joint Conference on Artificial Intelligence, IJCAI 2019 - Macao, China
Duration: 10 Aug 201916 Aug 2019

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2019-August
ISSN (Print)1045-0823

Conference

Conference28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Country/TerritoryChina
CityMacao
Period10/08/1916/08/19

Scopus Subject Areas

  • Artificial Intelligence

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