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arXiv 2102.12833cs.LG
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扩散型土动力装置的距离和分布埋置

Diffusion Earth Mover's Distance and Distribution Embeddings

Yale University(耶鲁大学);Université de Montréal(蒙特利尔大学);Mila – Quebec AI Institute(米拉-魁北克人工智能研究所)

Alexander Tong, Guillaume Huguet, Amine Natik, Kincaid MacDonald, Manik Kuchroo, Ronald Coifman, Guy Wolf, Smita Krishnaswamy

摘要:

我们提出了一种新的快速测量大量相关的高维数据集之间的距离称为扩散地球移动器的距离(EMD)的方法。我们将数据集建模为公共数据图上支持的分布,该公共数据图是从组合数据上计算的亲和矩阵导出的。在这种情况下,图是一个离散化的基本黎曼闭流形,我们证明了扩散EMD是拓扑等价的标准EMD测地线地面距离。扩散EMD可以在$\tilde{O}(n)$时间内计算,并且比类似的快速算法(例如基于树的EMD)更准确。我们还表明,扩散EMD是完全可微的,使其适合于未来在梯度下降框架中的使用,如深度神经网络。最后,我们展示了扩散EMD对从耶鲁纽黑文医院的210个COVID-19患者样本中收集的单细胞数据的应用。在这里,扩散EMD可以比同样精确的方法快至少两个数量级地导出细胞流形上患者之间的距离。患者之间的这种距离矩阵可以嵌入到更高级别的患者流形中,其揭示了患者的结构和异质性。更一般地说,扩散EMD适用于在许多医学和生物系统中并行大量收集的所有数据集。

英文摘要:

We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover's Distance (EMD). We model the datasets as distributions supported on common data graph that is derived from the affinity matrix computed on the combined data. In such cases where the graph is a discretization of an underlying Riemannian closed manifold, we prove that Diffusion EMD is topologically equivalent to the standard EMD with a geodesic ground distance. Diffusion EMD can be computed in $\tilde{O}(n)$ time and is more accurate than similarly fast algorithms such as tree-based EMDs. We also show Diffusion EMD is fully differentiable, making it amenable to future uses in gradient-descent frameworks such as deep neural networks. Finally, we demonstrate an application of Diffusion EMD to single cell data collected from 210 COVID-19 patient samples at Yale New Haven Hospital. Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods. This distance matrix between patients can be embedded into a higher level patient manifold which uncovers structure and heterogeneity in patients. More generally, Diffusion EMD is applicable to all datasets that are massively collected in parallel in many medical and biological systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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