Book contents
- Frontmatter
- Contents
- Preface
- Notation Used
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Probability Distributions
- 4 Statistical Inference
- 5 Linear Regression
- 6 Neural Networks
- 7 Non-linear Optimization
- 8 Learning and Generalization
- 9 Principal Components and Canonical Correlation
- 10 Unsupervised Learning
- 11 Time Series
- 12 Classification
- 13 Kernel Methods
- 14 Decision Trees, Random Forests and Boosting
- 15 Deep Learning
- 16 Forecast Verification and Post-processing
- 17 Merging of Machine Learning and Physics
- Appendices
- References
- Index
9 - Principal Components and Canonical Correlation
Published online by Cambridge University Press: 23 March 2023
Book contents
- Frontmatter
- Contents
- Preface
- Notation Used
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Probability Distributions
- 4 Statistical Inference
- 5 Linear Regression
- 6 Neural Networks
- 7 Non-linear Optimization
- 8 Learning and Generalization
- 9 Principal Components and Canonical Correlation
- 10 Unsupervised Learning
- 11 Time Series
- 12 Classification
- 13 Kernel Methods
- 14 Decision Trees, Random Forests and Boosting
- 15 Deep Learning
- 16 Forecast Verification and Post-processing
- 17 Merging of Machine Learning and Physics
- Appendices
- References
- Index
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.
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- Introduction to Environmental Data Science , pp. 283 - 329Publisher: Cambridge University PressPrint publication year: 2023