The situation is as follows. There are 400 examples in the training set and 200 discrete classes (each class has two examples). There are a few thousand attributes.
When I run dimensionality reduction to 2D or 3D, I would like to see (optimally) 200 clusters of 2 points each - one cluster for each class. However in practice that's not the case.
The question is, how do you go about choosing the set of attributes that will give optimal results with clustering/classification (whether with dimensionality reduction or without it).