Optimal transport for vector Gaussian mixture models

TL;DR

This paper explores optimal transport problems for vector-valued Gaussian mixture models, highlighting their computational efficiency and structural preservation benefits for applications like color imagery.

Contribution

It introduces a vectorized Gaussian mixture model framework for optimal mass transport, enhancing computational efficiency and structure preservation.

Findings

Vector Gaussian mixtures facilitate efficient optimal transport computations.

The approach preserves the structure of the original data.

Applications include color imagery and physical entity modeling.

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.