I'm working with a gesture dataset, where each gesture has a variable number of frames, and each frame has the 3d position of 20 joints, so that each gesture is represented by a matrix of size frames x 60.
I know that some joints are redundant, since for example knowing the position of both shoulders pretty much determines the position of the chest and viceversa, at least for the poses in the gestures in my dataset.
Running PCA on the matrix of all the gestures stacked horizontally, I get that with just 30 dimensions I can retain 99% of the variance, but of course this is in the eigenvectors space.
How can I select a subset of the joints (equivalently, features) and prove that the rest are redundant, in a PCA sort of way? The simplest thing I could think of was to select some joints, use them as basis, project the frames onto the space they generate, and use the result as features, but a) the classification experiments I did with that didn't turn out well and b) I've no way of formally justifying the removal of features/joints with that approach.