Convergence of Leray Cosheaves for Decorated Mapper Graphs
Algebraic Topology
2023-05-08 v2
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.
Keywords
Cite
@article{arxiv.2303.00130,
title = {Convergence of Leray Cosheaves for Decorated Mapper Graphs},
author = {Justin Curry and Washington Mio and Tom Needham and Osman Berat Okutan and Florian Russold},
journal= {arXiv preprint arXiv:2303.00130},
year = {2023}
}