Non-linear generative embeddings for kernels on latent variable models

Abstract

Generative embeddings use generative probabilistic models to project objects into a vectorial space of reduced dimensionality - where the so-called generative kernels can be defined. Some of these approaches employ generative models on latent variables to project objects into a feature space where the dimensions are related to the latent variables. Here, we propose to enhance the discriminative power of such spaces by performing a non-linear mapping of space dimensions leading to the formulation of novel generative kernels. In this paper, we investigate one possible non-linear mapping, based on a powering operation, able to equilibrate the contributions of each latent variable of the model, thus augmenting the entropy of the latent variables vectors. The validity of the idea has been shown in the case of two generative kernels, which have been evaluated with tests on shape recognition and gesture classification, with really satisfying results that outperform state-of-the-art methods.