MR-NTD: Manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation

Xutao Li*, Kwok Po NG, Gao Cong, Yunming Ye, Qingyao Wu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

85 Citations (Scopus)


With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.

Original languageEnglish
Article number7460200
Pages (from-to)1787-1800
Number of pages14
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number8
Publication statusPublished - Aug 2017

Scopus Subject Areas

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

User-Defined Keywords

  • Dimension reduction
  • manifold learning
  • nonnegative tensors


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