Convergence of Leray Cosheaves for Decorated Mapper Graphs

Justin Curry; Washington Mio; Tom Needham; Osman Berat Okutan; Florian Russold

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arXiv · 2303.00130

Convergence of Leray Cosheaves for Decorated Mapper Graphs

Justin Curry·Washington Mio·Tom Needham·Osman Berat Okutan·Florian Russold

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Abstract

We introduce decorated mapper graphs as a generalization of mapper graphs capable of capturing more topological information of a data set. A decorated mapper graph can be viewed as a discrete approximation of the cellular Leray cosheaf over the Reeb graph. We establish a theoretical foundation for this construction by showing that the cellular Leray cosheaf with respect to a sequence of covers converges to the actual Leray cosheaf as the resolution of the covers goes to zero.

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Justin Curry, Washington Mio, Tom Needham, Osman Berat Okutan, Florian Russold. 2023-02-28. Convergence of Leray Cosheaves for Decorated Mapper Graphs. https://arxiv.org/abs/2303.00130

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