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Topological data analysis investigates Gaussian persistence curves to enhance machine learning utility, suggesting stable transformations of diagrams.
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.
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Chung et al. (2026) studied this question.
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