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Does implementing pca to the training set considered as learning and adds VC dimension to the whole model?

I am currently using support vector machines to classify my inputs into 2 groups and I found out that the number of support vectors is very high (I have read some other posts about this problem and am considering to reduce the number of features in my input) but i am concerned that this might add complexity to my model as the model has to select the principal components

And is there a rule of thumb to selecting the optimal number of features to the number of training examples?

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