论文标题
Riemannian Block SPD耦合歧管及其在最佳运输中的应用
Riemannian block SPD coupling manifold and its application to optimal transport
论文作者
论文摘要
在这项工作中，我们研究了对称阳性（SPD）基质值测量措施之间的最佳运输（OT）问题。我们将上述提出为广义的最佳传输问题，在该问题中，成本，边缘和耦合表示为块矩阵，每个组件块都是SPD矩阵。耦合矩阵中的行块和列块的总和受到给定的块SPD边缘的约束。我们将这种块偶联矩阵赋予了一种新型的Riemannian歧管结构。这允许利用多功能的Riemannian优化框架来解决通用的SPD矩阵值问题。我们说明了拟议方法在几种应用中的有用性。
In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures. We formulate the above as a generalized optimal transport problem where the cost, the marginals, and the coupling are represented as block matrices and each component block is a SPD matrix. The summation of row blocks and column blocks in the coupling matrix are constrained by the given block-SPD marginals. We endow the set of such block-coupling matrices with a novel Riemannian manifold structure. This allows to exploit the versatile Riemannian optimization framework to solve generic SPD matrix-valued OT problems. We illustrate the usefulness of the proposed approach in several applications.
