论文标题
线性最佳运输嵌入：可证明的瓦瑟尔恒星分类，用于某些刚性转换和扰动
Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations
论文作者
论文摘要
在许多科学领域，分布之间的区分是一个重要的问题。这促使引入线性最佳运输（LOT），该运输（LOT）将分布空间嵌入到$ l^2 $ - 空间中。转换是通过计算每个分布到固定参考分布的最佳传输来定义的，并且在计算速度和确定分类边界时具有许多好处。在本文中，我们表征了许多设置，其中批次将分布属嵌入到线性分离的空间中。这在任意维度中是正确的，对于通过固定分布的偏移和尺度扰动而生成的分布族。我们还证明条件下，在这些分布之间，在任意维度的两个分布之间的$ l^2 $ l^2 $距离嵌入了两个分布之间的lot距离几乎是等等的。这是具有重大计算益处，因为一个人必须只计算$ n $最佳传输图来定义$ n $ n $分布之间的$ n^2 $成对距离。我们证明了许多对许多分配分类问题的好处。
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The transform is defined by computing the optimal transport of each distribution to a fixed reference distribution, and has a number of benefits when it comes to speed of computation and to determining classification boundaries. In this paper, we characterize a number of settings in which LOT embeds families of distributions into a space in which they are linearly separable. This is true in arbitrary dimension, and for families of distributions generated through perturbations of shifts and scalings of a fixed distribution.We also prove conditions under which the $L^2$ distance of the LOT embedding between two distributions in arbitrary dimension is nearly isometric to Wasserstein-2 distance between those distributions. This is of significant computational benefit, as one must only compute $N$ optimal transport maps to define the $N^2$ pairwise distances between $N$ distributions. We demonstrate the benefits of LOT on a number of distribution classification problems.
