I am performing a logistic regression on a rather big dataset (700k+ samples and 1k+ features). I suspect that a lot of these features will be highly correlated and multicollinearity can be an issue.
I believe that with elastic net regularisation is can perform feature selection and shrink the parameters of correlated features toghether (to prevent overfitting)
I understand that after PCA I end up with new (linnearly) uncorrelated (orthonal) features. I'm I correct to think that I now only need an L1 regularisation term in my optimazation function to have a simmular model as in the case with elastic net?
I prefer to do the PCA because I can reduce the number of parameters from 1k+ to around 60. (the rest of the PCs have 0 variance) which is more manageble to work with.
I am only interesed in a developing a prediction algorithm. I use R.