Canonical correlation analysis

Whitening and probabilistic canonical correlation analysis

CCA can also be viewed as a special whitening transformation where the random vectors ${\displaystyle X}$ and ${\displaystyle Y}$ are simultaneously transformed in such a way that the cross-correlation between the whitened vectors ${\displaystyle X^{CCA}}$ and ${\displaystyle Y^{CCA}}$ is diagonal. The canonical correlations are then interpreted as regression coefficients linking ${\displaystyle X^{CCA}}$ and ${\displaystyle Y^{CCA}}$ and may also be negative. The regression view of CCA also provides a way to construct a latent variable probabilistic generative model for CCA, with uncorrelated hidden variables representing shared and non-shared variability.