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Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?

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  • Hervé Cardot
  • David Degras

Abstract

Principal component analysis (PCA) is a method of choice for dimension reduction. In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to perform the PCA of streaming data and/or massive data. Despite the wide availability of recursive algorithms that can efficiently update the PCA when new data are observed, the literature offers little guidance on how to select a suitable algorithm for a given application. This paper reviews the main approaches to online PCA, namely, perturbation techniques, incremental methods and stochastic optimisation, and compares the most widely employed techniques in terms statistical accuracy, computation time and memory requirements using artificial and real data. Extensions of online PCA to missing data and to functional data are detailed. All studied algorithms are available in the  package onlinePCA on CRAN.

Suggested Citation

  • Hervé Cardot & David Degras, 2018. "Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?," International Statistical Review, International Statistical Institute, vol. 86(1), pages 29-50, April.
    • Handle: RePEc:bla:istatr:v:86:y:2018:i:1:p:29-50
    DOI: 10.1111/insr.12220
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    Cited by:

    1. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Jarek Duda, 2023. "Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series," Papers 2304.03069, arXiv.org, revised Apr 2023.
    3. A. Iodice D’Enza & A. Markos & F. Palumbo, 2022. "Chunk-wise regularised PCA-based imputation of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 365-386, June.
    4. Monnez, Jean-Marie & Skiredj, Abderrahman, 2021. "Widening the scope of an eigenvector stochastic approximation process and application to streaming PCA and related methods," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

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