Neural Computing and Applications

, Volume 31, Issue 12, pp 8327–8335 | Cite as

Unsupervised learning low-rank tensor from incomplete and grossly corrupted data

  • Zhijun Meng
  • Yaoming ZhouEmail author
  • Yongjia Zhao
Machine Learning - Applications & Techniques in Cyber Intelligence


Low-rank tensor completion and recovery have received considerable attention in the recent literature. The existing algorithms, however, are prone to suffer a failure when the multiway data are simultaneously contaminated by arbitrary outliers and missing values. In this paper, we study the unsupervised tensor learning problem, in which a low-rank tensor is recovered from an incomplete and grossly corrupted multidimensional array. We introduce a unified framework for this problem by using a simple equation to replace the linear projection operator constraint, and further reformulate it as two convex optimization problems through different approximations of the tensor rank. Two globally convergent algorithms, derived from the alternating direction augmented Lagrangian (ADAL) and linearized proximal ADAL methods, respectively, are proposed for solving these problems. Experimental results on synthetic and real-world data validate the effectiveness and superiority of our methods.


Unsupervised learning Low-rank tensor Tensor recovery Convex optimization Alternating direction augmented Lagrangian (ADAL) 



This work was supported by National Natural Science Foundation of China Nos. 61702023 and 91538204.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Aeronautic Science and EngineeringBeihang UniversityBeijingChina
  2. 2.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina
  3. 3.The State Key Laboratory of Virtual Reality Technology and SystemsBeijingChina

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