Likeness-Based dissimilarity measures for Gaussian Mixture Reduction and Data Fusion

In many practical contexts, Gaussian Mixtures are used as density approximators due to their versatility and representation capabilities. In some scenarios, it might be convenient to approximate a set of Gaussian densities with a single one, according to criteria which aim to preserve information while reducing the model complexity. This task can be seen as a particular case of the Gaussian Mixture Reduction problem, where the goal is to find a mixture of reduced size yielding the least dissimilarity from the original mixture. From a different perspective, this can be interpreted as a data fusion process, where several Gaussian densities are fused into one. In this work, an information-theoretic class of measures will be explored in the analytical and numerical properties in order to provide insights on their nature when adopted in a Gaussian mixture reduction or data fusion process.