Alternating proximal gradient method for sparse nonnegative Tucker decomposition

Yangyang Xu

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Multi-way data arises in many applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is to decompose a given tensor into the product of a core tensor and several factor matrices with sparsity and nonnegativity constraints. An alternating proximal gradient method is applied to solve the problem. The algorithm is then modified to sparse NTD with missing values. Per-iteration cost of the algorithm is estimated scalable about the data size, and global convergence is established under fairly loose conditions. Numerical experiments on both synthetic and real world data demonstrate its superiority over a few state-of-the-art methods for (sparse) NTD from partial and/or full observations. The MATLAB code along with demos are accessible from the author’s homepage.

Original languageEnglish (US)
Pages (from-to)39-70
Number of pages32
JournalMathematical Programming Computation
Issue number1
StatePublished - Mar 2015


  • Alternating proximal gradient method
  • Non-convex optimization
  • Sparse nonnegative Tucker decomposition
  • Sparse optimization

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