Discriminative probabilistic prototype learning

In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where an input datapoint is described by a set of feature vectors and its associated output may be given by soft labels indicating, for example, class probabilities. We represent an input datapoint as a K-dimensional vector, where each component is a mixture of probabilities over its corresponding set of feature vectors. Each probability indicates how likely a feature vector is to belong to one-out-of-K unknown prototype patterns. We propose a probabilistic model that parameterizes these prototype patterns in terms of hidden variables and therefore it can be trained with conventional approaches based on likelihood maximization. More importantly, both the model parameters and the prototype patterns can be learned from data in a discriminative way. We show that our model can be seen as a probabilistic generalization of learning vector quantization (LVQ). We apply our method to the problems of shape classification, hyperspectral imaging classification and people's work class categorization, showing the superior performance of our method compared to the standard prototype-based classification approach and other competitive benchmarks.