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Functional Data Analysis: An Introduction and Recent Developments.

Jan Gertheiss1, David Rügamer2,3, Bernard X W Liew4

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Summary
This summary is machine-generated.

Functional data analysis (FDA) provides tools for analyzing curves and functions, addressing challenges from high-dimensional data. This paper introduces key FDA methods and software for applications in medicine, neuroscience, and chemistry.

Keywords:
curve datafunctional regressionimage datalongitudinal data analysisobject‐oriented data analysis

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Area of Science:

  • Statistics
  • Data Science

Background:

  • Functional data analysis (FDA) extends statistical methods to curves, images, and functions.
  • High-dimensional nature of functional data presents unique analytical challenges.

Purpose of the Study:

  • Introduce fundamental concepts and techniques in FDA.
  • Describe software implementations and recent advancements in the field.
  • Demonstrate FDA methods with practical examples.

Main Methods:

  • Descriptive statistics, outlier detection, and smoothing for functional data.
  • Functional principal component analysis (FPCA) and functional regression.
  • Classification, clustering, and machine learning approaches for functional data.

Main Results:

  • Comprehensive overview of core FDA techniques.
  • Discussion of amplitude and phase variation, and statistical inference.
  • Application of methods using R software on human motion data.

Conclusions:

  • FDA methods are broadly applicable across scientific disciplines like medicine and neuroscience.
  • The paper provides accessible code and data for hands-on learning.
  • Sparse functional data methods are highlighted for longitudinal data analysis.