论文标题
快速的拓扑信号识别和持续的共同学周期匹配
Fast Topological Signal Identification and Persistent Cohomological Cycle Matching
论文作者
论文摘要
在拓扑数据分析的背景下，在许多应用程序中，识别拓扑意义和匹配信号的问题是重要且有用的推论任务。但是，现有解决方案对这些问题的局限性是计算速度。在本文中，我们通过研究使用共同学方法来确定拓扑流行和周期匹配的问题来利用持续同源计算的最新计算，从而提高了它们对更广泛的应用程序和上下文的可行性和适用性。我们在广泛的现实，大规模和复杂的数据集上演示了这一点。我们将现有的拓扑流行和周期匹配的概念扩展到包括一般的非Morse过滤。这提供了拓扑信号识别和持续周期匹配的最通用和灵活的最新适应，该适应在标准的机构HPC CPU设施中对数千个采样点进行了数千个采样点的订单比较。
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions to these problems, however, is computational speed. In this paper, we harness the state-of-the-art for persistent homology computation by studying the problem of determining topological prevalence and cycle matching using a cohomological approach, which increases their feasibility and applicability to a wider variety of applications and contexts. We demonstrate this on a wide range of real-life, large-scale, and complex datasets. We extend existing notions of topological prevalence and cycle matching to include general non-Morse filtrations. This provides the most general and flexible state-of-the-art adaptation of topological signal identification and persistent cycle matching, which performs comparisons of orders of ten for thousands of sampled points in a matter of minutes on standard institutional HPC CPU facilities.
