{"title":"Efficiently Approximating Spread Dimension with High Confidence","authors":"Kevin Dunne","doi":"arxiv-2408.14590","DOIUrl":null,"url":null,"abstract":"The concepts of spread and spread dimension of a metric space were introduced\nby Willerton in the context of quantifying biodiversity of ecosystems. In\nprevious work, we developed the theoretical basis for applications of spread\ndimension as an intrinsic dimension estimator. In this paper we introduce the\npseudo spread dimension which is an efficient approximation of spread\ndimension, and we derive a formula for the standard error associated with this\napproximation.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuanBio - Populations and Evolution","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14590","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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