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In Topological Data Analysis, persistence diagrams are useful tool for visualizing persistent homology. Set of diagrams endowed with Wasserstein distance and Bottleneck distance, form metric spaces which has several properties that make them useful for data analysis. In this paper we give a record on the development of concept of persistent homology and space of persistence diagrams.

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On the Space of Generalized Persistence Diagrams

  • 会议论文

  • 发表日期：

    2025年

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  • C. Jeeva Jose,
  • P. B. Vinod Kumar

摘要

In Topological Data Analysis, persistence diagrams are useful tool for visualizing persistent homology. Set of diagrams endowed with Wasserstein distance and Bottleneck distance, form metric spaces which has several properties that make them useful for data analysis. In this paper we give a record on the development of concept of persistent homology and space of persistence diagrams.