Dynamical Persistent Homology via Wasserstein Gradient Flow

Jinhui Xu; Minghua Wang

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arxiv 2412.03806 v1 pith:BYVWJIHL submitted 2024-12-05 math.AT cs.CG

Dynamical Persistent Homology via Wasserstein Gradient Flow

Minghua Wang , Jinhui Xu This is my paper

classification math.AT cs.CG

keywords datadiagramspersistenceanalysisgradientwassersteinadaptadvancement

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In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate variations in persistence diagrams back into the data space. This advancement enables direct manipulation of the data, guided by observed changes in persistence diagrams, offering a powerful tool for data analysis and interpretation in the context of topological data analysis.

Dynamical Persistent Homology via Wasserstein Gradient Flow

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