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1 results

  • 9 - Principal Components and Canonical Correlation

  • William W. Hsieh, University of British Columbia, Vancouver
  • Book:
    Introduction to Environmental Data Science
    Published online:
    23 March 2023
    Print publication:
    23 March 2023, pp 283-329

  • Summary

    Principal component analysis (PCA), a classical method for reducing the dimensionality of multivariate datasets, linearly combines the variables to generate new uncorrelated variables that maximize the amount of variance captured. Rotation of the PCA modes is commonly performed to provide more meaningful interpretation. Canonical correlation analysis (CCA) is a generalization of correlation (for two variables) to two groups of variables, with CCA finding modes of maximum correlation between the two groups. Instead of maximum correlation, maximum covariance analysis extracts modes with maximum covariance.