标题： 持久同调的蒸馏维也纳-里普斯滤波器和一种新的内存高效算法 显示英文标题

标题： The distilled Vietoris Rips filtration for persistent homology and a new memory efficient algorithm

摘要： 计算点云的维多利斯-里普斯持久同调所需的长时间计算时间和大内存需求仍然是其在大数据应用中的重大障碍。本文旨在减少这些计算的内存占用。它提出了一种新的构造，即精炼的维多利斯-里普斯滤波，并证明了其持久同调与标准维多利斯-里普斯的同调是同构的。精炼复形是通过在简化的维多利斯-里普斯复形上定义的离散莫尔斯向量场构建的。构建和简化精炼滤波边界矩阵的算法高度可并行化且内存效率高。只要给出成对距离矩阵，就可以在任何度量空间中的点云上实现该算法。 显示英文摘要

摘要： The long computational time and large memory requirements for computing Vietoris Rips persistent homology from point clouds remains a significant deterrent to its application to big data. This paper aims to reduce the memory footprint of these computations. It presents a new construction, the distilled Vietoris Rips filtration, and proves that its persistent homology is isomorphic to that of standard Vietoris Rips. The distilled complex is constructed using a discrete Morse vector field defined on the reduced Vietoris Rips complex. The algorithm for building and reducing the distilled filtration boundary matrix is highly parallelisable and memory efficient. It can be implemented for point clouds in any metric space given the pairwise distance matrix.