GEODESIC SINKHORN FOR FAST AND ACCURATE OPTIMAL TRANSPORT ON MANIFOLDS
GEODESIC SINKHORN FOR FAST AND ACCURATE OPTIMAL TRANSPORT ON MANIFOLDS
复制标题
用于在歧管上快速、准确、最佳运输的测地沉头
DOI：
10.1109/mlsp55844.2023.10285995
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Smita Krishnaswamy
中科院分区：
文献类型：
--
作者：
G. Huguet;Alexander Tong;María Ramos Zapatero;Guy Wolf;Smita Krishnaswamy
分布间最优传输距离的有效计算在数据科学中越来越重要。基于sinkhorn的方法目前是此类计算的最先进方法，但需要O（n2）次计算。此外，基于sinkhorn的方法通常使用数据点之间的欧几里得地面距离。然而，随着多种结构科学数据的流行，通常需要考虑测地线距离。在这里，我们通过提出基于在流形图上扩散热核的测地线sinkhorn来解决这两个问题。值得注意的是，测地线Sinkhorn只需要O（n log n）的计算，因为我们使用基于稀疏图拉普拉斯的切比雪夫多项式近似热核。我们将我们的方法应用于计算几个高维单细胞数据分布的质心，这些数据来自接受化疗的患者样本。特别地，我们把质心距离定义为两个质心之间的距离。使用这个定义，我们确定了与处理对蜂窝数据的影响相关的最佳传输距离和路径。
Efficient computation of optimal transport distance between distributions is of growing importance in data science. Sinkhorn-based methods are currently the state-of-the-art for such computations, but require O(n2) computations. In addition, Sinkhorn-based methods commonly use an Euclidean ground distance between datapoints. However, with the prevalence of manifold structured scientific data, it is often desirable to consider geodesic ground distance. Here, we tackle both issues by proposing Geodesic Sinkhorn—based on diffusing a heat kernel on a manifold graph. Notably, Geodesic Sinkhorn requires only O(n log n) computation, as we approximate the heat kernel with Chebyshev polynomials based on the sparse graph Laplacian. We apply our method to the computation of barycenters of several distributions of high dimensional single cell data from patient samples undergoing chemotherapy. In particular, we define the barycentric distance as the distance between two such barycenters. Using this definition, we identify an optimal transport distance and path associated with the effect of treatment on cellular data.
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DOI：
10.1101/2022.10.19.512668
发表时间：
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期刊：
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影响因子：
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作者：
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通讯作者：
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影响因子：
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发表时间：
2020-02
期刊：
Proceedings of machine learning research
影响因子：
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作者：
Alexander Tong;Jessie Huang;Guy Wolf;D. V. Dijk;Smita Krishnaswamy
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DOI：
10.1109/icassp43922.2022.9746556
发表时间：
2022-05
期刊：
Proceedings of the ... IEEE International Conference on Acoustics, Speech, and Signal Processing. ICASSP (Conference)
影响因子：
--
作者：
Tong, Alexander;Huguet, Guillaume;Shung, Dennis;Natik, Amine;Kuchroo, Manik;Lajoie, Guillaume;Wolf, Guy;Krishnaswamy, Smita
通讯作者：
Krishnaswamy, Smita