Jiening Zhu

Jung Hun Oh, Rena Elkin, Anish Kumar Simhal et al.

The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT into widely used probabilistic models, such as Gaussian or Gaussian mixture, have been developed to enhance the capability of modeling complex multimodal densities of real datasets. However, very few studies have explored the OMT problems in a reproducing kernel Hilbert space (RKHS), wherein the kernel trick is utilized to avoid the need to explicitly map input data into a high-dimensional feature space. In the current study, we propose a Wasserstein-type metric to compute the distance between two Gaussian mixtures in a RKHS via the kernel trick, i.e., kernel Gaussian mixture models.

Jiening Zhu, Kaiming Xu, Allen Tannenbaum

Vector-valued Gaussian mixtures form an important special subset of vector-valued distributions. In general, vector-valued distributions constitute natural representations for physical entities, which can mutate or transit among alternative manifestations distributed in a given space. A key example is color imagery. In this note, we vectorize the Gaussian mixture model and study several different optimal mass transport related problems associated to such models. The benefits of using vector Gaussian mixture for optimal mass transport include computational efficiency and the ability to preserve structure.