Maximum Entropy Generative Models for Similarity-based Learning

A generative model for similarity-based classification is proposed using maximum entropy estimation. First, a descriptive set of similarity statistics is assumed to be sufficient for classification. Then the class conditional distributions of these descriptive statistics are estimated as the maximum entropy distributions subject to empirical moment constraints. The resulting exponential class conditional distributions are used in a maximum a posteriori decision rule, forming the similarity discriminant analysis (SDA) classifier. The relationship between SDA and the quadratic discriminant analysis classifier is discussed. An example SDA classifier is given that uses the class centroids as the descriptive statistics. Compared to the nearest-centroid classifier, which is also based only on the class centroids, simulation and experimental results show SDA consistently improves performance.