@inproceedings{5219,
  title = {Fast Newton-type Methods for the Least Squares Nonnegative Matrix Approximation Problem},
  journal = {Proceedings of the SIAM International Conference on Data Mining (SDM 2007)},
  booktitle = {SDM 2007},
  abstract = {Nonnegative Matrix Approximation is an effective matrix
  decomposition technique that has proven to be useful for a
  wide variety of applications ranging from document analysis
  and image processing to bioinformatics. There exist a few
  algorithms for nonnegative matrix approximation (NNMA),
  for example, Lee & Seung’s multiplicative updates, alternating
  least squares, and certain gradient descent based procedures.
  All of these procedures suffer from either slow convergence,
  numerical instabilities, or at worst, theoretical unsoundness.
  In this paper we present new and improved algorithms
  for the least-squares NNMA problem, which are
  not only theoretically well-founded, but also overcome many
  of the deficiencies of other methods. In particular, we use
  non-diagonal gradient scaling to obtain rapid convergence.
  Our methods provide numerical results superior to both Lee
  & Seung’s method as well to the alternating least squares
  (ALS) heuristic, which is known to work well in some situations
  but has no theoretical guarantees (Berry et al. 2006).
  Our approach extends naturally to include regularization and
  box-constraints, without sacrificing convergence guarantees.
  We present experimental results on both synthetic and realworld
  datasets to demonstrate the superiority of our methods,
  in terms of better approximations as well as efficiency.},
  pages = {343-354},
  editors = {Apte, C. },
  publisher = {Society for Industrial and Applied Mathematics},
  organization = {Max-Planck-Gesellschaft},
  institution = {Society for Industrial and Applied Mathematics},
  school = {Biologische Kybernetik},
  address = {Pittsburgh, PA, USA},
  month = apr,
  year = {2007},
  slug = {5219},
  author = {Kim, D. and Sra, S. and Dhillon, I.},
  month_numeric = {4}
}