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, as well as material science and cancer research.

翻译：Mapper与Ball Mapper是拓扑数据分析工具，用于探索高维点云并可视化其上定义的标量值函数。受纽结理论中未解决问题的启发，我们在Ball Mapper中新增了用于编码点云结构、内部关系及对称性的功能。此外，通过融合Mapper与Ball Mapper的构造优势，我们开发了一种可比较单一数据集高维数据描述符的工具。这种新型混合算法（Ball Mapper上的Mapper）适用于高维透镜函数。作为概念验证，我们将其应用于纽结理论、博弈论、材料科学及癌症研究领域。