Optimal transport for vector Gaussian mixture models

2020/12/16 by Jiening Zhu, Zhu, Jiening, Kaiming Xu +3
Mathematics · Biochemistry, Genetics and Molecular Biology · #Point processes and geometric inequalities #Markov Chains and Monte Carlo Methods #Diffusion and Search Dynamics

paper · pdf · doi:10.48550/arxiv.2012.09226

Abstract

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.

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• A note on two problems in connexion with graphs

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