Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization

Qiquan Shi, Yiu Ming CHEUNG*, Qibin Zhao, Haiping LU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

45 Citations (Scopus)


Multidimensional data (i.e., tensors) with missing entries are common in practice. Extracting features from incomplete tensors is an important yet challenging problem in many fields such as machine learning, pattern recognition, and computer vision. Although the missing entries can be recovered by tensor completion techniques, these completion methods focus only on missing data estimation instead of effective feature extraction. To the best of our knowledge, the problem of feature extraction from incomplete tensors has yet to be well explored in the literature. In this paper, we therefore tackle this problem within the unsupervised learning environment. Specifically, we incorporate low-rank tensor decomposition with feature variance maximization (TDVM) in a unified framework. Based on orthogonal Tucker and CP decompositions, we design two TDVM methods, TDVM-Tucker and TDVM-CP, to learn low-dimensional features viewing the core tensors of the Tucker model as features and viewing the weight vectors of the CP model as features. TDVM explores the relationship among data samples via maximizing feature variance and simultaneously estimates the missing entries via low-rank Tucker/CP approximation, leading to informative features extracted directly from observed entries. Furthermore, we generalize the proposed methods by formulating a general model that incorporates feature regularization into low-rank tensor approximation. In addition, we develop a joint optimization scheme to solve the proposed methods by integrating the alternating direction method of multipliers with the block coordinate descent method. Finally, we evaluate our methods on six real-world image and video data sets under a newly designed multiblock missing setting. The extracted features are evaluated in face recognition, object/action classification, and face/gait clustering. Experimental results demonstrate the superior performance of the proposed methods compared with the state-of-the-art approaches.

Original languageEnglish
Article number8513841
Pages (from-to)1803-1817
Number of pages15
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number6
Publication statusPublished - Jun 2019

Scopus Subject Areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

User-Defined Keywords

  • Feature extraction
  • feature regularization
  • incomplete tensor
  • low-rank tensor completion
  • orthogonal tensor decomposition
  • variance maximization


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