Mapper-type algorithms for complex data and relations
This provides a new tool for researchers in fields like material science and cancer research to analyze complex data, though it is incremental as it builds on existing Topological Data Analysis methods.
The paper tackled the challenge of exploring high-dimensional data by enhancing Ball Mapper to encode structures, relations, and symmetries, and combining it with Mapper to compare data descriptors, resulting in a hybrid algorithm applicable to various fields like knot theory and cancer research.
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.