| The use of covariance matrices in dimension reduction for space-time data |
| Outline of talk |
| PCA and EOFs |
| PCA – some definitions, terminology |
| Finding PCs/EOFs |
| PCA in atmospheric science (geoscience) |
| Example – northern hemisphere sea level pressure (NH SLP) |
| Slide 8 |
| Example 2 – NH 850hPa streamfunction |
| Slide 10 |
| Choices in PCA |
| Covariance or correlation |
| Covariance or correlation II |
| How many PCs/EOFs? |
| Choice of normalisation constraint |
| Simplification |
| Simplification II |
| Rotation |
| Example of rotation– USA summer precipitation |
| Slide 20 |
| Other Simplification Methods |
| Slide 22 |
| Slide 23 |
| Relationships between variables in two (or more) groups |
| Canonical correlation analysis (CCA) |
| Maximum covariance analysis |
| Maximum covariance analysis: Pacific SST vs. Hemispheric 500mb height ( Wallace et al., 1992) |
| Extensions to 3 (or more) modes |
| O-mode, P-mode, É, T-mode |
| Extended EOF analysis |
| MEEOF example – 5 variables averaged over 0-10¡ S for various longitudes |
| Concluding remarks |
| More concluding remarks |
| Slide 34 |
| Discrete set of values for loadings |
| LASSO-based approach |
| LASSO II |
| Mediterranean sea surface temperature example |
| SST example |
| Slide 40 |
| Slide 41 |
| Other techniques for two groups of variables |
| Three mode PCA |