Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?. (5th July 2017)

• Record Type: Journal Article
• Authors: Cardot, Hervé; Degras, David
• Is Part Of: International statistical review. Volume 86:Number 1(2018)
• Page Start: 29
• Page End: 50
• Publication Date: 2017-07-05
• Subjects: Eigenvalue decomposition -- perturbation methods -- stochastic gradient -- generalised Hebbian algorithm -- incremental SVD; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12220
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: 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 packageonlinePCA on CRAN.