论文标题
带有R-K图和重力波分析的拓扑图理论的新方法
A Novel Approach to Topological Graph Theory with R-K Diagrams and Gravitational Wave Analysis
论文作者
论文摘要
图理论和拓扑数据分析虽然功能强大，但具有许多缺点，这些缺点与TDA和图形网络分析的敏感性和一致性有关。在本文中，我们旨在提出一种新的方法，用于编码数据点之间的矢量关联，以实现图和拓扑数据分析之间的平滑过渡。 We conclusively reveal effective ways of converting such vectorized associations to simplicial complexes representing micro-states in a Phase-Space, resulting in filter specific, homotopic self-expressive, event-driven unique topological signatures which we have referred as Roy-Kesselman Diagrams or R-K Diagrams with persistent homology, which emerge from filter-based encodings of R-K Models.该方法的有效性和影响是针对Ligo Open Science Center发布的最新LIGO数据集的高维原始和得出的重力波数据测量的测试，同时还测试了使用Tableau SuperStore Sales Sales数据集证明的非科学用例的通用方法。我们认为，我们的工作结果将为许多未来的科学和工程应用奠定基础，这些科学和工程应用具有稳定的高维数据分析，并具有拓扑图理论转换的综合有效性。
Graph Theory and Topological Data Analytics, while powerful, have many drawbacks related to their sensitivity and consistency with TDA & Graph Network Analytics. In this paper, we aim to propose a novel approach for encoding vectorized associations between data points for the purpose of enabling smooth transitions between Graph and Topological Data Analytics. We conclusively reveal effective ways of converting such vectorized associations to simplicial complexes representing micro-states in a Phase-Space, resulting in filter specific, homotopic self-expressive, event-driven unique topological signatures which we have referred as Roy-Kesselman Diagrams or R-K Diagrams with persistent homology, which emerge from filter-based encodings of R-K Models. The validity and impact of this approach were tested specifically on high-dimensional raw and derived measures of Gravitational Wave Data from the latest LIGO datasets published by the LIGO Open Science Centre along with testing a generalized approach for a non-scientific use-case, which has been demonstrated using the Tableau Superstore Sales dataset. We believe the findings of our work will lay the foundation for many future scientific and engineering applications of stable, high-dimensional data analysis with the combined effectiveness of Topological Graph Theory transformations.
