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<p>New local ultrametricity measures for finite metric data are proposed through the viewpoint that their Vietoris-Rips corners are samples from <i>p</i>-adic Mumford curves endowed with a Radon measure coming from a regular differential 1-form. This is experimentally applied to three datasets.</p>

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On the Local Ultrametricity of Finite Metric Data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月25日

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  • Patrick Erik Bradley

摘要

New local ultrametricity measures for finite metric data are proposed through the viewpoint that their Vietoris-Rips corners are samples from p-adic Mumford curves endowed with a Radon measure coming from a regular differential 1-form. This is experimentally applied to three datasets.