Computing nonnegative tensor factorizations

M. P. Friedlander and K. Hatz

Optimization Methods and Software, 23(4):631-647, August 2008

Abstract

Nonnegative tensor factorization (NTF) is a technique for computing a parts-based representation of high-dimensional data. NTF excels at exposing latent structures in datasets, and at finding good low-rank approximations to the data. We describe an approach for computing the NTF of a dataset that relies only on iterative linear-algebra techniques and that is comparable in cost to the nonnegative matrix factorization. (The better-known nonnegative matrix factorization is a special case of NTF and is also handled by our implementation.) Some important features of our implementation include mechanisms for encouraging sparse factors and for ensuring that they are equilibrated in norm. The complete Matlab software package is available under the GPL license.

BibTeX

@article{FrieHatz:2008,
  Author =       {M. P. Friedlander and K. Hatz},
  Month =        {March},
  Journal =      {Computational Optimization and Applications},
  Title =        {Computing Nonnegative Tensor Factorizations},
  Year =         2008,
  abstract =     {Nonnegative tensor factorization (NTF) is a
                  technique for computing a parts-based representation
                  of high-dimensional data. NTF excels at exposing
                  latent structures in datasets, and at finding good
                  low-rank approximations to the data. We describe an
                  approach for computing the NTF of a dataset that
                  relies only on iterative linear-algebra techniques
                  and that is comparable in cost to the nonnegative
                  matrix factorization. (The better-known nonnegative
                  matrix factorization is a special case of NTF and is
                  also handled by our implementation.) Some important
                  features of our implementation include mechanisms
                  for encouraging sparse factors and for ensuring that
                  they are equilibrated in norm. The complete Matlab
                  software package is available under the GPL
                  license.},
  volume =       23,
  number =       4,
  pages =        {631-647},
  DOI =          {10.1080/10556780801996244},
}