支架和脊柱：使用覆盖树，局部主成分分析和持久同源性组织高维数据
Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology
摘要：
我们提出了一种灵活的多尺度方法，用于组织，可视化和理解从分层空间或附近采样的数据集。该算法的第一部分结合多尺度局部主成分分析和拓扑数据分析，使用自适应阈值生成覆盖树。所得到的覆盖树节点由分层空间的同一层内或附近的点组成。然后将它们连接以形成\emph{scaffolding}图，然后将其简化并折叠成\emph{spine}图。从后一个图中，分层结构变得明显。我们展示了我们的技术在几个合成点云的例子，我们用它来理解音乐音频数据中的歌曲结构。
英文摘要：
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a combination of multi-scale local principal component analysis and topological data analysis. The resulting cover tree nodes consist of points within or near the same stratum of the stratified space. They are then connected to form a \emph{scaffolding} graph, which is then simplified and collapsed down into a \emph{spine} graph. From this latter graph the stratified structure becomes apparent. We demonstrate our technique on several synthetic point cloud examples and we use it to understand song structure in musical audio data.
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。
