A Non-parametric Fisher Kernel.

In this manuscript, we derive a non-parametric version of the Fisher kernel. We obtain this original result from the Non-negative Matrix Factorization with the Kullback-Leibler divergence. By imposing suitable normalization conditions on the obtained factorization, it can be assimilated to a mixture of densities, with no assumptions on the distribution of the parameters. The equivalence between the Kullback-Leibler divergence and the log-likelihood leads to kernelization by simply taking partial derivatives. The estimates provided by this kernel, retain the consistency of the Fisher kernel.