Enrique G Alvarado, Robin Belton, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine, Sarah Tymochko
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The Mapper algorithm is a popular tool for visualization and data exploration
in topological data analysis. We investigate an inverse problem for the Mapper
algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of
Mapper parameters such that the output Mapper graph of $X$ is isomorphic to
$G$? We provide constructions that affirmatively answer this question. Our
results demonstrate that it is possible to engineer Mapper parameters to
generate a desired graph.
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