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<p>Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a persistence diagram. To utilize machine and deep learning methods, these diagrams are summarized by transforming them into functions. In this paper we investigate the stability and injectivity of a class of smooth, one-dimensional functional summaries called Gaussian persistence curves.</p>

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Gaussian Persistence Curves

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月23日

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  • Yu-Min Chung,
  • Michael Hull,
  • Austin Lawson,
  • Neil Pritchard

摘要

Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a persistence diagram. To utilize machine and deep learning methods, these diagrams are summarized by transforming them into functions. In this paper we investigate the stability and injectivity of a class of smooth, one-dimensional functional summaries called Gaussian persistence curves.