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.

翻译：矢量价值高斯混合物是矢量价值分布的重要特殊子集,一般而言,矢量价值分布是物理实体的自然体现,这些实体可在某一空间分布的替代表现形式之间发生变异或中转,一个关键例子是彩色图像。在本说明中,我们将高斯混合物模型病媒化,并研究与此类模型有关的几种与最佳大众迁移有关的不同的最佳问题。利用矢量高斯混合物进行最佳大众迁移的好处包括计算效率和保护结构的能力。