CCA, SVD and Multivariate regression^*

Sometimes, one may want to extend the spatial correlation studies to the coupling between two multivariate fields, both with several observations.

We will use the matrix ${\bf Y}$ to refer to the time series of $\vec{y}(t)$, where the vectors are given as the columns of ${\bf Y}$. The two data fields ${\bf Y}$ and ${\bf X}$, contain data which are sampled at p and q locations respectively over a time period with n measurements at each location:

 

$${\bf Y} = [\vec{y}_1, \vec{y}_2, .. \vec{y}_n],$$

$${\bf X} = [\vec{x}_1, \vec{x}_2, .. \vec{x}_n].$$ (8.19)