提出一种新型Wasserstein距离，可有效匹配潜在高斯分布的几何结构。
Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions
- 基于改进的Benamou-Brenier方法，引入等距不变性约束
- 高斯分布间距离等价于其特征值有序向量的欧氏距离
- 适用于潜在空间中高斯分布的恢复与对齐任务
我们提出一种改进的Benamou-Brenier型方法，构建一种具有全局等距不变性的Wasserstein型距离。该距离通过惩罚粒子轨迹方向与速度不变时的无代价运动来定义。我们证明，对于高斯分布，该距离可简化为有序特征值向量间的欧氏距离，并展示了其在恢复潜在高斯分布中的直接应用。
原文摘要 · Abstract (English)
We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions.
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