Robust tensor completion using transformed tensor singular value decomposition

Guangjing Song; Michael K. Ng; Xiongjun Zhang

doi:10.1002/nla.2299

journal article Mar 18, 2020

Robust tensor completion using transformed tensor singular value decomposition

Guangjing Song Michael K. Ng

Xiongjun Zhang

Numerical Linear Algebra with Applications Vol. 27 No. 3 · Wiley

View at Publisher Save 10.1002/nla.2299

Abstract

SummaryIn this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal‐to‐noise ratio than that by using Fourier transform and other robust tensor completion methods.

Topics

No keywords indexed for this article. Browse by subject →

References

55

[1]

Tensor Completion for Estimating Missing Values in Visual Data

Przemyslaw Musialski, Peter Wonka, Jieping Ye

IEEE Transactions on Pattern Analysis and Machine... 10.1109/tpami.2012.39

[2]

10.1016/j.patrec.2011.11.015

[3]

10.1007/978-3-662-04186-4

[4]

10.1016/j.sigpro.2019.04.029

[5]

10.1109/tgrs.2017.2670021

[6]

10.1016/j.cam.2019.06.004

[7]

10.1109/msp.2013.2297439

[8]

10.1016/j.aml.2019.04.019

[9]

10.1007/s10915-019-01044-8

[10]

KoldaT. G.andSunJ. Scalable tensor decompositions for multi‐aspect data mining. Paper presented at: Proceedings of the 8th International Conference on Data Mining;2008. p. 363–372. 10.1109/icdm.2008.89

[11]

MiwakeichiF Valdes‐SosaPA Aubert‐VazquezE et al. Decomposing EEG data into space‐time‐frequency components using parallel factor analysis and its relation with cerebral blood flow. Paper presented at: Proceedings of the International Conference on Neural Information Processing;2007. pages 802–810. 10.1007/978-3-540-69158-7_83

[12]

10.1073/pnas.0709146104

[13]

RabanserS ShchurO GünnemannS. Introduction to tensor decompositions and their applications in machine learning. arXiv:1711.10781;2017.

[14]

10.1109/tpami.2017.2734888

[15]

10.1109/tnnls.2018.2872583

[16]

FazelM. Matrix rank minimization with applications [PhD thesis]. Stanford University;2002.

[17]

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

Benjamin Recht, Maryam Fazel, Pablo A. Parrilo

SIAM Review 10.1137/070697835

[18]

Robust principal component analysis?

Emmanuel J. Candès, Xiaodong Li, Yi Ma et al.

Journal of the ACM 10.1145/1970392.1970395

[19]

10.1007/s10208-009-9045-5

[20]

10.1109/tit.2015.2415195

[21]

10.1109/tit.2015.2401574

[22]

Recht B "A simpler approach to matrix completion" J Mach Learn Res (2009)

[23]

Hitchcock FL "The expression of a tensor or a polyadic as a sum of products" Stud Appl Math (1927)

[24]

Tensor Decompositions and Applications

Tamara G. Kolda, Brett W. Bader

SIAM Review 10.1137/07070111x

[25]

JainP OhS. Provable tensor factorization Q4 with missing data. Paper presented at: Proceedings of the Neural Information Processing Systems;2014. p.1431‐1439.

[26]

10.1016/j.parco.2015.10.002

[27]

Tensor-Train Decomposition

I. V. Oseledets

SIAM Journal on Scientific Computing 10.1137/090752286

[28]

10.1109/tip.2017.2672439

[29]

Some Mathematical Notes on Three-Mode Factor Analysis

Ledyard R Tucker

Psychometrika 10.1007/bf02289464

[30]

Romera‐ParedesB PontilM. A new convex relaxation for tensor completion. Paper presented at: Proceedings of the Neural Information Processing Systems;2013. p.2967‐2975.

[31]

MuC HuangB WrightJ andGoldfarbD. Square deal: Lower bounds and improved relaxations for tensor recovery. InProc. Int. Conf. Mach. Learn. volume 32 pages 73–81 2014.

[32]

Tensor completion and low-n-rank tensor recovery via convex optimization

Silvia Gandy, Benjamin Recht, Isao Yamada

Inverse Problems 10.1088/0266-5611/27/2/025010

[33]

GuQ GuiH HanJ. Robust tensor decomposition with gross corruption. Paper presented at: Proceedings of the Neural Information Processing Systems;2014. p.1422‐1430.

[34]

Huang B "Provable models for robust low‐rank tensor completion" Pac J Optim (2015)

[35]

Factorization strategies for third-order tensors

Misha E. Kilmer, Carla D. Martin

Linear Algebra and its Applications 10.1016/j.laa.2010.09.020

[36]

10.1016/j.laa.2015.07.021

[37]

10.1137/110841229

[38]

Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging

Misha E. Kilmer, Karen Braman, Ning Hao et al.

SIAM Journal on Matrix Analysis and Applications 10.1137/110837711

[39]

ZhangZ ElyG AeronS HaoN andKilmerM. Novel methods for multilinear data completion and de‐noising based on tensor‐SVD. Paper presented at: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition;2014. p. 3842–3849. 10.1109/cvpr.2014.485

[40]

10.1137/18m1202311

[41]

10.1109/tsp.2016.2639466

[42]

Tensor Factorization for Low-Rank Tensor Completion

Pan Zhou, Canyi Lu, Zhouchen Lin et al.

IEEE Transactions on Image Processing 10.1109/tip.2017.2762595

[43]

10.1109/tnnls.2016.2611525

[44]

JiangQ NgMK. Robust low‐tubal‐rank tensor completion via convex optimization. Paper presented at: Proceedings of the 28th International Joint Conferences on Artificial Intelligence;2019. p. 2649–2655. 10.24963/ijcai.2019/368

[45]

10.1109/tpami.2019.2891760

[46]

10.1109/tit.2011.2104999

[47]

10.1007/s10107-016-1007-5

[48]

10.1007/s10107-014-0850-5

[49]

10.1137/15m1048008

[50]

10.1111/rssb.12244

Showing 50 of 55 references

Cited By

192

Tensor Robust Principal Component Analysis via Tensor Fibered Rank and \({\boldsymbol{{l_p}}}\) Minimization

Kaixin Gao, Zheng-Hai Huang · 2023

SIAM Journal on Imaging Sciences

Sparse Nonnegative Tensor Factorization and Completion With Noisy Observations

Xiongjun Zhang, Michael K. Ng · 2022

IEEE Transactions on Information Th...

Nonlocal robust tensor recovery with nonconvex regularization *

Duo Qiu, Minru Bai · 2021

Inverse Problems

Robust Low Transformed Multi-Rank Tensor Methods for Image Alignment

Duo Qiu, Minru Bai · 2021

Journal of Scientific Computing

Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion

Tai-Xiang Jiang, Michael K. Ng · 2020

IEEE Transactions on Image Processi...

Metrics

192

Citations

55

References

Details

Published: Mar 18, 2020
Vol/Issue: 27(3)
License: View

Authors

G

Guangjing Song

School of Mathematics and Information Sciences Weifang University Weifang China

M

Michael K. Ng

Department of Mathematics The University of Hong Kong Pokfulam Hong Kong

X

Xiongjun Zhang

School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences Central China Normal University Wuhan China

Funding

National Natural Science Foundation of China Award: 11571098

Fundamental Research Funds for the Central Universities Award: CCNU19ZN017

University of Hong Kong Award: 104005583

Cite This Article

Guangjing Song, Michael K. Ng, Xiongjun Zhang (2020). Robust tensor completion using transformed tensor singular value decomposition. Numerical Linear Algebra with Applications, 27(3). https://doi.org/10.1002/nla.2299

Robust tensor completion using transformed tensor singular value decomposition

You May Also Like