Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport

17 Jul 2020 Divol Vincent DATASHAPE Lacombe Théo DATASHAPE

Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of discrete measures, and by observing that its metrics can be expressed as optimal partial transport problems, we introduce a generalization of persistence diagrams, namely Radon measures supported on the upper half plane... (read more)

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Categories


  • COMPUTATIONAL GEOMETRY
  • GEOMETRIC TOPOLOGY