标题： ALBATROSS：基于随机子采样的廉价过滤几何方法 显示英文标题

标题： ALBATROSS: Cheap Filtration Based Geometry via Stochastic Sub-Sampling

摘要： 拓扑数据分析（TDA）检测生物数据中的几何结构。 然而，许多TDA算法内存需求高，在大规模数据集上不实用。 在这里，我们介绍一种统计协议，减少了TDA的内存需求，并使拥有适度计算资源的科学家能够使用。 我们通过两个经验数据集验证该协议，表明它以更低的内存需求复制了之前的发现。 最后，我们通过在高空间分辨率下映射人类皮层的功能相关性拓扑结构，展示了该协议的强大功能，这是在没有这种新方法之前无法实现的。 显示英文摘要

摘要： Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory requirements and gives access to scientists with modest computing resources. We validate this protocol against two empirical datasets, showing that it replicates previous findings with much lower memory requirements. Finally, we demonstrate the power of the protocol by mapping the topology of functional correlations for the human cortex at high spatial resolution, something that was previously infeasible without this novel approach.