当前位置：
X-MOL 学术
›
Proc. Am. Math. Soc.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
The space of persistence diagrams on 𝑛 points coarsely embeds into Hilbert space
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-22 , DOI: 10.1090/proc/15363 Atish Mitra , Žiga Virk
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-22 , DOI: 10.1090/proc/15363 Atish Mitra , Žiga Virk
Abstract:We prove that the space of persistence diagrams on 
points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dimension 
. Such an embedding enables utilisation of Hilbert space techniques on the space of persistence diagrams. We also prove that when the number of points is not bounded, the corresponding spaces of persistence diagrams do not have finite asymptotic dimension. Furthermore, in the case of the bottleneck distance, the corresponding space does not coarsely embed into Hilbert space.
中文翻译：
𝑛点上的余辉图空间粗略地嵌入到希尔伯特空间
摘要：我们证明了点的持久性图空间（具有瓶颈或Wasserstein距离）通过证明它的渐近维数而粗略地嵌入到希尔伯特空间中。这样的嵌入使得能够在余辉图的空间上利用希尔伯特空间技术。我们还证明了，当点数不受限制时，持续图的相应空间就没有有限的渐近维数。此外，在瓶颈距离的情况下，相应的空间不会粗糙地嵌入希尔伯特空间。
更新日期：2021-04-22
points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dimension . Such an embedding enables utilisation of Hilbert space techniques on the space of persistence diagrams. We also prove that when the number of points is not bounded, the corresponding spaces of persistence diagrams do not have finite asymptotic dimension. Furthermore, in the case of the bottleneck distance, the corresponding space does not coarsely embed into Hilbert space. 中文翻译：
𝑛点上的余辉图空间粗略地嵌入到希尔伯特空间
摘要：我们证明了
点的持久性图空间（具有瓶颈或Wasserstein距离）通过证明它的渐近维数而粗略地嵌入到希尔伯特空间中。这样的嵌入使得能够在余辉图的空间上利用希尔伯特空间技术。我们还证明了，当点数不受限制时，持续图的相应空间就没有有限的渐近维数。此外，在瓶颈距离的情况下，相应的空间不会粗糙地嵌入希尔伯特空间。
京公网安备 11010802027423号