[2109.00831] Mapper-type algorithms for complex data and relationships

Download the PDF of the paper entitled “Mapper-type Algorithms for Complex Data and Relationships” by Pawe{\l} D{\l}otko and one other author

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overview: Mapper and Ball Mapper are topological data analysis tools used to explore high-dimensional point clouds and visualize scalar-valued functions in those point clouds. Inspired by open problems in knot theory, new features have been added to Ball Mapper that allow encoding of point group structure, internal relations, and symmetries. Furthermore, we combine the strengths of the Mapper and Ball Mapper constructs to create a tool for comparing high-dimensional data descriptors of a single dataset. This new hybrid algorithm, Mapper on Ball Mapper, can be applied to high-dimensional lens functions. Proof-of-concept applications include knots, game theory, materials science, and cancer research.