Principal component analysis for big data

Jianqing Fan Qiang Sun WenXin Zhou Ziwei Zhu

Statistics Theory and Methods mathscidoc:1912.43365

Wiley StatsRef: Statistics Reference Online, 1-13
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting statistical inference. Principal component analysis, commonly referred to as PCA, has become an essential tool for multivariate data analysis and unsupervised dimension reduction, the goal of which is to find a lower dimensional subspace that captures most of the variation in the dataset. This article provides an overview of methodological and theoretical developments of PCA over the past decade, with focus on its applications to big data analytics. We first review the mathematical formulation of PCA and its theoretical development from the view point of perturbation analysis. We then briefly discuss the relationship between PCA and factor analysis as well as its applications to
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  title={Principal component analysis for big data},
  author={Jianqing Fan, Qiang Sun, WenXin Zhou, and Ziwei Zhu},
  booktitle={Wiley StatsRef: Statistics Reference Online},
Jianqing Fan, Qiang Sun, WenXin Zhou, and Ziwei Zhu. Principal component analysis for big data. In Wiley StatsRef: Statistics Reference Online. pp.1-13.
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