Non-linear generative embeddings for kernels on latent variable models

Generative embeddings use generative probabilisticmodels to project objects into a vectorial space of reduceddimensionality – where the so-called generative kernels canbe defined. Some of these approaches employ generativemodels on latent variables to project objects into a feature space where the dimensions are related to the latentvariables. Here, we propose to enhance the discriminativepower of such spaces by performing a non-linear mappingof space dimensions leading to the formulation of novel generative kernels. In this paper, we investigate one possiblenon-linear mapping, based on a powering operation, ableto equilibrate the contributions of each latent variable ofthe model, thus augmenting the entropy of the latent variables vectors. The validity of the idea has been shown in thecase of two generative kernels, which have been evaluatedwith tests on shape recognition and gesture classification,with really satisfying results that outperform state-of-theart methods.