Mapper–Type Algorithms for Complex Data and Relations
该文在拓扑数据分析工具Ball Mapper中增加新功能以编码点云的结构与内部关系，并融合Mapper与Ball Mapper构建混合算法Mapper on Ball Mapper，用于比较同一数据集的高维描述符，适用于高维透镜函数，并以纽结理论和博弈论为例验证。
Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar–valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to Ball Mapper that enable encoding of the structure, internal relations and symmetries of the point cloud. Moreover, the strengths of Mapper and Ball Mapper constructions are combined to create a tool for comparing high dimensional data descriptors of a single dataset. This new hybrid algorithm, Mapper on Ball Mapper, is applicable to high dimensional lens functions. As a proof of concept we include applications to knot and game theory.