I have a data set of 932 responses (carbon emissions) with p=21 features (Temperature, net radiation, photon flux density, soil water content etc.) that may have some influence on them.
I am using scikit learn's DecisionTreeRegressor and the Docs suggest using PCA to help narrow down the number of features to look at. Some of my factors are definitely highly correlated eg. net radiation and photon flux so using PCA sounds like a good idea.
I understand the general principal of PCA, but I'm having a hard time finding any information of how I should use PCA to do this. Should I use the first n principal components as the input features for the regression tree? Here is a plot of the explained variance ratio for my dataset generated using scikit's PCA:
Once of the pro's of CART is that trees are easy to interpret, but I don't see how that result would be easy to explain or be applicable to any other data sets? Or is there some standard way to use the principal components to identify the most "important" factors? I've seen mention of using the correlation between factors and the first n principal components but I can't seem to find anything on it now. Anything to help point me in the right direction would be greatly appreciated!