I have a 100x45 dataset and I'd like to perform feature selection and classification/regression.
I'm currently using various techniques to check which one has the best performances, but I have a doubt about how to treat PCA + SVM or random Forest or CART. With other feature selection methods and elastic net, I'm performing Cross Validation (CV) to select the hyperparameters and to test the model, since I have few records and at the moment I'm not in the condition to increase them.
With PCA which is the best course of action? Train-test or CV? Should I perform PCA on the train set and then use the number of PCs on the test set? In the case of CV how can I proceed?