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Simple Poisson PCA: an algorithm for (sparse) feature extraction with simultaneous dimension determination

Author

Listed:
  • Luke Smallman

    (Cardiff University)

  • William Underwood

    (University of Oxford)

  • Andreas Artemiou

    (Cardiff University)

Abstract

Dimension reduction tools offer a popular approach to analysis of high-dimensional big data. In this paper, we propose an algorithm for sparse Principal Component Analysis for non-Gaussian data. Since our interest for the algorithm stems from applications in text data analysis we focus on the Poisson distribution which has been used extensively in analysing text data. In addition to sparsity our algorithm is able to effectively determine the desired number of principal components in the model (order determination). The good performance of our proposal is demonstrated with both synthetic and real data examples.

Suggested Citation

  • Luke Smallman & William Underwood & Andreas Artemiou, 2020. "Simple Poisson PCA: an algorithm for (sparse) feature extraction with simultaneous dimension determination," Computational Statistics, Springer, vol. 35(2), pages 559-577, June.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00903-0
    DOI: 10.1007/s00180-019-00903-0
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    References listed on IDEAS

    as
    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    L0 penalty; Exponential family; Text data analysis; Dimension reduction;
    All these keywords.

    JEL classification:

    • L0 - Industrial Organization - - General

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