Selecting features manually and proving the rest are redundant 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.
 A: I assume you mean "some features are redundant for classification", in that they do not contain andy class discriminatory information.
If you want to preserve class-discriminatory information while reducing dimension, you should use Linear Discriminant Analysis. PCA is not suited for this. Below is a copy/paste from Wikipedia.

LDA is closely related to principal component analysis (PCA) and
  factor analysis in that they both look for linear combinations of
  variables which best explain the data.[4] LDA explicitly attempts to
  model the difference between the classes of data. PCA on the other
  hand does not take into account any difference in class, and factor
  analysis builds the feature combinations based on differences rather
  than similarities. Discriminant analysis is also different from factor
  analysis in that it is not an interdependence technique: a distinction
  between independent variables and dependent variables (also called
  criterion variables) must be made.
LDA works when the measurements made on independent variables for each
  observation are continuous quantities. When dealing with categorical
  independent variables, the equivalent technique is discriminant
  correspondence analysis.[5][6]

