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