I am studying some factorial methods, namely, PCA and Correspondence Analysis and I have a few questions for you.
It is clear that the principal axes in PCA are linear combinations of the original variables of the dataset. Thus, it is always possible to "reverse" the procedure, that is, go back from the axes of maximum inertia to the original features, like well explained in this thread.
On the other hand, the situation is less clear as regards to CA. I cannot really get how the axis of maximum inertia are related to the original variables and if it is possible to "reverse" the procedure as it is for PCA.
Furthermore, I have another doubt. When I apply PCA or other methods (e.g. MCA) to make feature selection for a classification problem, which variables should I use for the model? Should I use the ones obtained by the factorial method (combination of the original ones) or the original variables that result in contributing the most in the creation of the principal axes?
