Feature Selection by Maximum Marginal Diversity: Optimality and Implications for Visual Recognition

We address the question of feature selection in the context of visual recognition. It is shown that, besides efficient from a computational standpoint, the infomax principle is nearly optimal in the minimum Bayes error sense. The concept of marginal diversity is introduced, lead-ing to a generic principle for feature selection (the principle of maximum marginal diversity) of extreme computational simplicity. The relation-ships between infomax and the maximization of marginal diversity are identified, uncovering the existence of a family of classification proce-dures for which near optimal (in the Bayes error sense) feature selection does not require combinatorial search. Examination of this family in light of recent studies on the statistics of natural images suggests that visual recognition problems are a subset of it.