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A very fast algorithm for matrix factorization

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  • Nikulin, Vladimir
  • Huang, Tian-Hsiang
  • Ng, Shu-Kay
  • Rathnayake, Suren I.
  • McLachlan, Geoffrey J.

Abstract

We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an ever-increasing demand for methods of dimension reduction in order to undertake the statistical analysis of interest. Our algorithm uses a gradient-based approach which can be used with an arbitrary loss function provided the latter is differentiable. The speed and effectiveness of our algorithm for dimension reduction is demonstrated in the context of supervised classification of some real high-dimensional data sets from the bioinformatics literature.

Suggested Citation

  • Nikulin, Vladimir & Huang, Tian-Hsiang & Ng, Shu-Kay & Rathnayake, Suren I. & McLachlan, Geoffrey J., 2011. "A very fast algorithm for matrix factorization," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 773-782, July.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:773-782
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    3. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
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