以高信度有效逼近传播维度

arXiv - QuanBio - Populations and Evolution Pub Date : 2024-08-26 DOI:arxiv-2408.14590

Kevin Dunne

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引用次数: 0

摘要

威勒顿（Willerton）在量化生态系统的生物多样性时提出了度量空间的扩散和扩散维度的概念。在之前的工作中，我们为作为内在维度估计器的扩散维度的应用奠定了理论基础。在本文中，我们引入了伪展宽维度，它是展宽维度的有效近似值，我们还推导出了与该近似值相关的标准误差公式。

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Efficiently Approximating Spread Dimension with High Confidence

The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. In previous work, we developed the theoretical basis for applications of spread dimension as an intrinsic dimension estimator. In this paper we introduce the pseudo spread dimension which is an efficient approximation of spread dimension, and we derive a formula for the standard error associated with this approximation.

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arXiv - QuanBio - Populations and Evolution

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