Continuous mixture modeling via goodness-of-fit ridges

We present a novel method for representing “extruded” distributions. An extruded distribution is an M-dimensional manifold in the parameter space of the component distribution. Representations of that manifold are “continuous mixture models”. We present a method for forming one-dimensional continuous Gaussian mixture models of sampled extruded Gaussian distributions via ridges of goodness-of-fit. Using Monte Carlo simulations and ROC analysis, we explore the utility of a variety of binning techniques and goodness-of-fit functions. We demonstrate that extruded Gaussian distributions are more accurately and consistently represented by continuous Gaussian mixture models than by finite Gaussian mixture models formed via maximum likelihood expectation maximization.