Sparse non-negative tensor factorization using columnwise coordinate descent

Ji Liu*, Jun Liu*, Peter Wonka, Jieping Ye

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


Many applications in computer vision, biomedical informatics, and graphics deal with data in the matrix or tensor form. Non-negative matrix and tensor factorization, which extract data-dependent non-negative basis functions, have been commonly applied for the analysis of such data for data compression, visualization, and detection of hidden information (factors). In this paper, we present a fast and flexible algorithm for sparse non-negative tensor factorization (SNTF) based on columnwise coordinate descent (CCD). Different from the traditional coordinate descent which updates one element at a time, CCD updates one column vector simultaneously. Our empirical results on higher-mode images, such as brain MRI images, gene expression images, and hyperspectral images show that the proposed algorithm is 12 orders of magnitude faster than several state-of-the-art algorithms.

Original languageEnglish (US)
Pages (from-to)649-656
Number of pages8
JournalPattern Recognition
Issue number1
StatePublished - Jan 2012


  • Columnwise coordinate descent
  • Non-negative
  • Sparse
  • Tensor factorization

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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