Mathematics of PCR and CCA Simon Mason simoniri
- Slides: 8
Mathematics of PCR and CCA Simon Mason simon@iri. columbia. edu Seasonal Forecasting Using the Climate Predictability Tool
Principal Components Regression Instead of using the original data as predictors, we can use the principal components as predictors in the same simple linear regression (SLR) model. The PCR option contains the information in many of the original predictors, and so a complex MLR model can be simplified considerably: 2 Seasonal Forecasting Using the Climate Predictability Tool
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Canonical Correlation Analysis (CCA) • The weights VX and VY are defined so that ZX and ZY have maximum correlation. R is diagonal matrix of correlations. The current SSTs are represented by x. • In CPT, the CCA is performed using principal components of X and Y to avoid over-fitting. • Suitable for multiple predictors, and multiple predictands. • Predictions are spatially consistent. 7 Seasonal Forecasting Using the Climate Predictability Tool
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