A survey of functional principal component analysis

Abstract

Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a new area of statistics, functional data analysis extends existing methodologies and theories from the realms of functional analysis, generalized linear model, multivariate data analysis, nonparametric statistics, regression models and many others. From both methodological and practical viewpoints, this paper provides a review of functional principal component analysis, and its use in explanatory analysis, modeling and forecasting, and classification of functional data.

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Acknowledgments

The author thanks the editor and two reviewers for their insightful comments, which led to a substantial improvement of the manuscript. The author thanks Professor Rob Hyndman for introducing him to the field of functional data analysis.

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Shang, H.L. A survey of functional principal component analysis. AStA Adv Stat Anal 98, 121–142 (2014). https://doi.org/10.1007/s10182-013-0213-1

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Keywords

  • Dimension reduction
  • Explanatory analysis
  • Functional data clustering
  • Functional data modeling
  • Functional data forecasting