Approximating Persistent Homology for Large Datasets. (arXiv:2204.09155v2 [stat.ML] UPDATED)

Persistent homology is an important methodology from topological data
analysis which adapts theory from algebraic topology to data settings and has
been successfully implemented in many applications. It produces a statistical
summary in the form of a persistence diagram, which captures the shape and size
of the data. Despite its widespread use, persistent homology is simply
impossible to implement when a dataset is very large. In this paper we address
the problem of finding a representative persistence diagram for prohibitively …

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