The general aim of this work is to learn a unique statistical signature for the state of a particular speech pathology. We pose this as a speaker identification problem for dysarthric individuals. To that end, we propose a novel algorithm for feature selection that aims to minimize the effects of speaker-specific features (e.g., fundamental frequency) and maximize the effects of pathology-specific features (e.g., vocal tract distortions and speech rhythm). We derive a cost function for optimizing feature selection that simultaneously trades off between these two competing criteria. Furthermore, we develop an efficient algorithm that optimizes this cost function and test the algorithm on a set of 34 dysarthric and 13 healthy speakers. Results show that the proposed method yields a set of features related to the speech disorder and not an individual's speaking style. When compared to other feature-selection algorithms, the proposed approach results in an improvement in a disorder fingerprinting task by selecting features that are specific to the disorder.