Nonnegative Matrix Factorization

with Alternating Nonnegativity-constrained Least Squares and Block Principal Pivoting / Active Set Methods.
This page provides MATLAB software for efficient nonnegative matrix factorization (NMF) algorithms based on alternating non-negativity constrained least squares.
Software

MATLAB software: DOWNLOAD Last modified on Feb. 20, 2010

Summary of package:
  • Plain, sparse, and regularized NMFs are all included and can be easily selected.
  • Both the block principal pivoting and the active set methods are provided in a single program and can be easily selected. Once you download the above file, see instructions to select an algorithm.
  • Key subroutines are fast algorithms for nonnegativity-constrained least squares problem, which maybe of interest to many applications other than NMF.
The details of the implemented algorithms are described in the following papers.
  • Fast Nonnegative Matrix Factorization: An Active-set-like Method And Comparisons,
    Jingu Kim and Haesun Park,
    SIAM Journal on Scientific Computing (SISC), 33(6), pp. 3261-3281, 2011
    PDF

  • Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons,
    Jingu Kim and Haesun Park,
    In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, pp. 353-362, 2008.
    PDF SLIDES

  • Nonnegative Matrix Factorization Based on Alternating Non-negativity-constrained Least Squares and the Active Set Method,
    Hyunsoo Kim and Haesun Park,
    SIAM Journal on Matrix Analysis and Applications, 30(2):713-730, 2008.
    PDF


  • Sparse Non-negative Matrix Factorizations via Alternating Non-negativity-constrained Least Squares for Microarray Data Analysis,
    Hyunsoo Kim and Haesun Park,
    Bioinformatics, 23-12:1495-1502, 2007.
    PDF

Nonnegative Tensor Factorization

Canonical Decomposition / PARAFAC with Nonnegativity Constraints
Software

MATLAB software: DOWNLOAD Last modified on Mar. 27, 2012

Requirement:
  • Installation of MATLAB Tensor Toolbox is required. The version of the toolbox with which this software was tested is 2.4.
Summary of package:
  • The block principal pivoting method, the active-set method, the hierarchical alternating least squares (HALS) method, and the multiplicative updating method are included. See above paper for more descriptions.
The details of the implemented algorithms are described in the following paper.
  • Fast Nonnegative Tensor Factorization with an Active-set-like Method.,
    Jingu Kim and Haesun Park,
    In High-Performance Scientific Computing: Algorithms and Applications, Springer, pp. 311-326, 2012.
    PDF URL

  • A Lecture on NMF and NTF
    A Keynote Talk at 2011 SIAM International Conference on Data Mining

  • Related Publications

    Other papers related to NMF using these algorithms are as follows.
    • Sparse Nonnegative Matrix Factorization for Clustering,
      Jingu Kim and Haesun Park,
      Georgia Tech Technical Report GT-CSE-08-01, 2008.
      PDF

    • A Fast Algorithm for Nonnegative Tensor Factorization using Block Coordiante Descent and Adtiveset-Like Method ,
      K. Balasubramanian, J. Kim, A. Puretskiy, M. Berry, and H. Park,
      Text Mining Workshop, SIAM International Conference on Data Mining, 2010
      PDF
    Related Webpages
    Feedback

    Please email to Jingu Kim (jingu@cc.gatech.edu) with any questions in using the code, bug reports, or comments.
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