How to perform feature selection on dataset with categorical and numerical features? I am working on a dataset with 30 columns (29 numerical, 1 non-ordinal categorical). I hot-encoded the categorical feature and reached at 35 columns. To improve training efficiency, I want to perform feature selection on my dataset. However , I am confused with how to handle a dataset with categorical and numerical features combined.

I read that it is not reasonable to apply PCA on dummies given they are discrete. Is it reasonable to apply PCA first on numerical features then concatenate them with dummies?
I tried to implement recursive feature elemination with cross-validation (RFECV) to the entire feature space. But I don't think it is reasonable to remove some but not all dummy features given they are generated out of one category.

Any suggestions? Any help is appreciated.
python pandas scikit-learn feature-selection
It is fine to apply feature selection technique on one hot encoded variables. Because if one particular segment of that variable is correlated with your target, then it is a good news. Your model will understand the scenario better.
Or, You can label encode your categorical variable first so that you still have 30 variables (29 numerical + 1 label-encoded categorical variable). Now try to find the importance value of each variable, and take the relevant ones (Use any method for it: be it RFE, random forest feature selection, pearson's correlation etc). Once you have the final list of variables, and the label-encoded variable is also coming as relevant, it is ok to put it into the model.