Feature selection by maximum marginal diversity: optimality and implications for visual recognition

We have recently shown that: 1) the infomax principle for the organization of perceptual systems leads to visual recognition architectures that are nearly optimal in the minimum Bayes error sense, and 2) a quantity which plays an important role in infomax solutions is the marginal diversity (MD) - the average distance between the class-conditional density of each feature and their mean. Since MD is a discriminant quantity and can be computed with great efficiency, the principle of maximum marginal diversity (MMD) was suggested for discriminant feature selection. In this paper, we study the optimality (in the infomax sense) of the MMD principle and analyze its effectiveness for feature selection in the context of visual recognition. In particular, 1) we derive a close form relation between the optimal infomax and MMD solutions, and 2) show that there is a family of classification problems for which the two are identical. Examination of this family in light of recent studies on the statistics of natural images suggests that the equivalence conditions are likely to hold for the problem of visual recognition. We present experimental evidence supporting the conclusions that: 1) MD is a good predictor for the recognition ability of a given set of features; 2) MMD produces features that are more discriminant than those obtained with currently predominant criteria such as energy compaction; and 3) the extracted features are detectors of visual attributes that are perceptually relevant for low-level image classification.