Assume I have a set of N vectors with M features each. If I want to create a latent space to project these vectors into, there are a variety of techniques available to me, such as Principle Component Analysis (PCA).
However, if I were using PCA and I decide to only consider x of M features for a latent space, I would then have to carry out PCA again for the N vectors with x features each.
Is there an unsupervised learning technique which allows for training with N vectors of M features, but allows for selection of a subset of M features with completely recomputing the space? Is my only option to carry out PCA for all possible subsets of M which might be considered and cache the results? Is there a different term for what I'm trying to do?