Keywords: Persistent Homology, Topological Data Analysis, Multi-Parameter Persistence
TL;DR: Multi-Parameter Persistent Homology is Practical
Abstract: Multi-parameter persistent homology is a branch of topological data analysis that is notorious for being more difficult than the standard (one-parameter) version, both in theory and for algorithmic problems. We report on three ongoing projects that demonstrates that multi-parameter method are applicable to large data sets. For instance, natural bi-filtrations generalizing Vietoris-Rips or alpha filtrations for hundred of thousands of points can be decomposed within seconds in their indecomposable parts.
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