Given a $m\times p$ matrix $Y$ on the left, and a $m\times q$ matrix $X$ on the right, CCA tries to find 2 sets of mapping coefficients such that $Y\beta_{l}$ and $X\beta_{r}$ have the highest possible correlation.
This resembles a multi-target regression problem that is trying to minimize the norm of $Y-X\cdot [\beta_{1},\beta_{2},...,\beta_{p}]$.
So, my question is, what's the relationship between canonical correlation analysis and multi-target (multivariate) regression?
Can anyone give any insight here? if possible, from an application perspective?
