{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T19:37:13Z","timestamp":1769024233888,"version":"3.49.0"},"reference-count":91,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T00:00:00Z","timestamp":1661817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"ARC Discovery Grant","doi-asserted-by":"publisher","award":["DP170102472"],"award-info":[{"award-number":["DP170102472"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000923","name":"ARC Discovery Grant","doi-asserted-by":"publisher","award":["18H03296"],"award-info":[{"award-number":["18H03296"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]},{"name":"JSPS Kakenhi Kiban (B) Research Grant","award":["DP170102472"],"award-info":[{"award-number":["DP170102472"]}]},{"name":"JSPS Kakenhi Kiban (B) Research Grant","award":["18H03296"],"award-info":[{"award-number":["18H03296"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Properties of data distributions can be assessed at both global and local scales. At a highly localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which assesses growth rates of the cumulative distribution function within a restricted neighborhood and characterizes properties of the geometry of a local neighborhood. In this paper, we explore the connection of LID to other well known measures for complexity assessment and comparison, namely, entropy and statistical distances or divergences. In an asymptotic context, we develop analytical new expressions for these quantities in terms of LID. This reveals the fundamental nature of LID as a building block for characterizing and comparing data distributions, opening the door to new methods for distributional analysis at a local scale.<\/jats:p>","DOI":"10.3390\/e24091220","type":"journal-article","created":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T21:25:18Z","timestamp":1661894718000},"page":"1220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Local Intrinsic Dimensionality, Entropy and Statistical Divergences"],"prefix":"10.3390","volume":"24","author":[{"given":"James","family":"Bailey","sequence":"first","affiliation":[{"name":"School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC 3010, Australia"}]},{"given":"Michael E.","family":"Houle","sequence":"additional","affiliation":[{"name":"School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC 3010, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2099-4973","authenticated-orcid":false,"given":"Xingjun","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer Science, Fudan University, Shanghai 200437, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/j.sigpro.2012.09.003","article-title":"Divergence measures for statistical data processing\u2014An annotated bibliography","volume":"93","author":"Basseville","year":"2013","journal-title":"Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Houle, M.E. 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