In this question I ask what is a reasonable dimension for a vector in the Bag of Features model. since k is big and so the number of dimensions is too big to be managed efficiently, PCA is performed in order to reduce the number of dimensions. What is the usual resulting vector dimension (related to the starting k -dimension vector) in such an application?
Usually, PCA is not used.
Because you then lose sparsity. For performance reasons you want to have sparse vectors, so don't use PCA.