The fact that Recursive CCS finds strictly more than one good direction means that CCS is not efficient at locating all information related to truth: it is not able to find a direction which contains as much information as the direction found by taking the difference of the means. Note: Logistic Regression seems to be about as leaky as CCS.

Perhaps a naive question, but if a single linear projection exists that contains the desired information, why isn't this 'global minimum' found with LR (or CSS)?