IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i7p773-782.html
   My bibliography  Save this article

A very fast algorithm for matrix factorization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(11)00039-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lago, Jesus & De Ridder, Fjo & Vrancx, Peter & De Schutter, Bart, 2018. "Forecasting day-ahead electricity prices in Europe: The importance of considering market integration," Applied Energy, Elsevier, vol. 211(C), pages 890-903.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rosember Guerra-Urzola & Katrijn Van Deun & Juan C. Vera & Klaas Sijtsma, 2021. "A Guide for Sparse PCA: Model Comparison and Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 893-919, December.
    2. Guerra Urzola, Rosember & Van Deun, Katrijn & Vera, J. C. & Sijtsma, K., 2021. "A guide for sparse PCA : Model comparison and applications," Other publications TiSEM 4d35b931-7f49-444b-b92f-a, Tilburg University, School of Economics and Management.
    3. Zura Kakushadze & Willie Yu, 2020. "Machine Learning Treasury Yields," Papers 2003.05095, arXiv.org.
    4. Nicolas Jouvin & Pierre Latouche & Charles Bouveyron & Guillaume Bataillon & Alain Livartowski, 2021. "Greedy clustering of count data through a mixture of multinomial PCA," Computational Statistics, Springer, vol. 36(1), pages 1-33, March.
    5. Shen, Dan & Shen, Haipeng & Marron, J.S., 2013. "Consistency of sparse PCA in High Dimension, Low Sample Size contexts," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 317-333.
    6. Landgraf, Andrew J. & Lee, Yoonkyung, 2020. "Dimensionality reduction for binary data through the projection of natural parameters," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    7. Jesús Arroyo & Elizaveta Levina, 2022. "Overlapping Community Detection in Networks via Sparse Spectral Decomposition," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 1-35, June.
    8. Zhang, Lingsong & Lu, Shu & Marron, J.S., 2015. "Nested nonnegative cone analysis," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 100-110.
    9. Zura Kakushadze & Willie Yu, 2020. "Machine Learning Treasury Yields," Bulletin of Applied Economics, Risk Market Journals, vol. 7(1), pages 1-65.
    10. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    11. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    12. P Fogel & C Geissler & P Cotte & G Luta, 2022. "Applying separative non-negative matrix factorization to extra-financial data," Working Papers hal-03689774, HAL.
    13. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
    14. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    15. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
    16. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    17. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    18. Spelta, A. & Pecora, N. & Rovira Kaltwasser, P., 2019. "Identifying Systemically Important Banks: A temporal approach for macroprudential policies," Journal of Policy Modeling, Elsevier, vol. 41(1), pages 197-218.
    19. Adele Ravagnani & Fabrizio Lillo & Paola Deriu & Piero Mazzarisi & Francesca Medda & Antonio Russo, 2024. "Dimensionality reduction techniques to support insider trading detection," Papers 2403.00707, arXiv.org, revised May 2024.
    20. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:773-782. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.