Linear optimal transport embedding: provable Wasserstein classification for certain rigid transformations and perturbations
Linear optimal transport embedding: provable Wasserstein classification for certain rigid transformations and perturbations
复制标题
线性最优传输嵌入：针对某些刚性变换和扰动的可证明 Wasserstein 分类
DOI：
10.1093/imaiai/iaac023
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Cloninger, Alexander
中科院分区：
文献类型：
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作者：
Moosmüller, Caroline;Cloninger, Alexander
区分分布是许多科学领域中的一个重要问题。这促使线性最优运输（LOT）的引入，它将分布空间嵌入到空间中。该变换通过计算每个分布到固定参考分布的最佳传输来定义，并且在计算速度和确定分类边界方面具有许多好处。在本文中，我们描述了一些设置中，LOT嵌入家庭的分布到一个空间中，他们是线性可分的。这在任意维中都是正确的，对于通过固定分布的移位和缩放的扰动产生的分布族也是如此。我们还证明了两个分布在任意维上的LOT嵌入距离与两个分布之间的Wasserstein-2距离近似等距的条件。这是一个重要的计算优势，因为我们只需要计算最优的传输图来定义分布之间的成对距离。我们证明了LOT的好处，一些分布分类问题。
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-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 thedistance 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 computeoptimal transport maps to define thepairwise distances betweendistributions. We demonstrate the benefits of LOT on a number of distribution classification problems.