  In this paper we propose a simple yet powerful method for learning
representations in supervised learning scenarios where each original input
datapoint is described by a set of vectors and their associated outputs may be
given by soft labels indicating, for example, class probabilities. We represent
an input datapoint as a mixture of probabilities over the corresponding set of
feature vectors where each probability indicates how likely each vector is to
belong to an unknown prototype pattern. 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
benchmark methods.
