论文标题
一个新的压缩盖树，用于k-neartible搜索和点云的稳定范围的合并图
A new compressed cover tree for k-nearest neighbour search and the stable-under-noise mergegram of a point cloud
论文作者
论文摘要
本文由两个与计算几何形状有关的主题和与拓扑数据分析有关的一个主题，该主题结合了计算几何学和代数拓扑的领域，用于分析数据。第一部分研究了在任何度量空间中较大的n个参考点中找到k最近的邻居的经典问题。第二部分是关于在任何有限度量空间上建造最小跨越树（MST）。第三部分将持久性的关键概念扩展在拓扑数据分析中，朝着新的方向扩展。
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies the classical problem of finding k nearest neighbors to m query points in a larger set of n reference points in any metric space. The second part is about the construction of a Minimum Spanning Tree (MST) on any finite metric space. The third part extends the key concept of persistence within Topological Data Analysis in a new direction.
