Intrinsic dimension of geometric data sets

DOI10.2748/tmj.20201015azbMath1491.68188arXiv1801.07985OpenAlexW4210349949MaRDI QIDQ2075416

Tom Hanika, Gerd Stumme, Friedrich Martin Schneider

Publication date: 14 February 2022

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.07985

zbMATH Keywords

dimension functionmachine learningobservable distancedimension cursegeometric data sets

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Data structures (68P05) Computational aspects of data analysis and big data (68T09)

Related Items (1)

Scaling dimension

Uses Software

• UCI-ml

Cites Work

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• On the geometry of similarity search: dimensionality curse and concentration of measure
• Uniform spaces and measures
• Metric measure geometry. Gromov's theory of convergence and concentration of metrics and measures
• An axiomatic approach to intrinsic dimension of a dataset
• Estimate of observable diameter of \(l_p\)-product spaces
• Lipschitz functions on topometric spaces
• A Topological Application of the Isoperimetric Inequality
• Formal Concept Analysis of Social Networks
• Metric measure limits of spheres and complex projective spaces
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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