分层空间学习：重构嵌入图
Stratified Space Learning: Reconstructing Embedded Graphs
摘要：
许多数据丰富的行业对大型数据集的结构的有效发现和建模感兴趣，因为它允许对嵌入在高维空间中的大量数据进行快速分类和降维。这些基础结构的建模也有利于创建更好地代表真实数据的模拟数据。特别是，在使用真实数据流可能证明不切实际或不受欢迎的情况下进行系统测试。我们试图通过拓扑数据分析与数值建模相结合的方法来发现和建模结构。作为结合这两个领域的第一步，我们检查的抽象图$G$结构的恢复，并模型的线性嵌入$|G|$只给出一个嘈杂的点云样本$X$的$|G|$。
英文摘要：
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional spaces. The modelling of these underlying structures is also beneficial for the creation of simulated data that better represents real data. In particular, for systems testing in cases where the use of real data streams might prove impractical or otherwise undesirable. We seek to discover and model the structure by combining methods from topological data analysis with numerical modelling. As a first step in combining these two areas, we examine the recovery of the abstract graph $G$ structure, and model a linear embedding $|G|$ given only a noisy point cloud sample $X$ of $|G|$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
