k-MLE for mixtures of generalized Gaussians

We introduce an extension of the k-MLE algorithm, a fast algorithm for learning statistical mixture models relying on maximum likelihood estimators, which allows to build mixture of generalized Gaussian distributions without a fixed shape parameter. This allows us to model finely probability density functions which are made of highly non Gaussian components. We theoretically prove the local convergence of our method and show experimentally that it performs comparably to Expectation-Maximization methods while being more computationally efficient.