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<p>In this paper, we present a methodology for detecting outliers and testing the goodness-of-fit of random sets using topological data analysis. We construct a filtration from the sublevel sets of the signed distance function and consider various summary functions of the persistence diagrams derived from the obtained persistent homology. Outliers are detected using functional depths for the summary functions. Global envelope tests, employing these summary statistics as test statistics, were used to construct the goodness-of-fit test. The procedures were justified by a simulation study using germ-grain random set models and application to real data concerning histological images of mastopathic and mammary cancer breast tissue.</p>

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Topological data analysis for random sets and its application in detecting outliers and goodness of fit testing

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Vesna Gotovac Ɖogaš,
  • Marcela Mandarić

摘要

In this paper, we present a methodology for detecting outliers and testing the goodness-of-fit of random sets using topological data analysis. We construct a filtration from the sublevel sets of the signed distance function and consider various summary functions of the persistence diagrams derived from the obtained persistent homology. Outliers are detected using functional depths for the summary functions. Global envelope tests, employing these summary statistics as test statistics, were used to construct the goodness-of-fit test. The procedures were justified by a simulation study using germ-grain random set models and application to real data concerning histological images of mastopathic and mammary cancer breast tissue.