  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.
