I got two multidimensional datasets, X and Y. I thought I build the model, which explains the relationship between two datasets, using canonical correlation analysis (CCA). The first correlation between two components(canonical variates) is 0.87. I think which is not so bad.
The problem is I have to do regression. For example, how does Y change what if a new X' comes in. So I need to get new components of Y, and then reconstruct it like the original Y.
I am not good at this area, so I can't do anything right now.
For more information, originally the dataset X has only categorical variables, so I vectorized it into binary (= One-hot encoding). And Y has 6 variables.
It seems to be related to Reduced-Rank Regression or Partial Least Squares as far as I know. And if you give me some examples of this using R, it would be much helpful and much appreciated.