An axiomatic approach to intrinsic dimension of a dataset

DOI10.1016/j.neunet.2007.12.030zbMath1254.68102arXiv0712.2063OpenAlexW1489992831WikidataQ51895521 ScholiaQ51895521MaRDI QIDQ1931997

Vladimir G. Pestov

Publication date: 17 January 2013

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2063

zbMATH Keywords

featuresconcentration of measurecurse of dimensionalityGromov distancehigh-dimensional noiseintrinsic dimension of datasetsrandom sample of a manifoldspace with metric and measure

Mathematics Subject Classification ID

Searching and sorting (68P10) Learning and adaptive systems in artificial intelligence (68T05)

Related Items (9)

Is the \(k\)-NN classifier in high dimensions affected by the curse of dimensionality? ⋮ Anderson relaxation test for intrinsic dimension selection in model-based clustering ⋮ Intrinsic dimension estimation: relevant techniques and a benchmark framework ⋮ Lower bounds on performance of metric tree indexing schemes for exact similarity search in high dimensions ⋮ Indexability, concentration, and VC theory ⋮ Dimension estimation using weighted correlation dimension method ⋮ Intrinsic dimension estimation: advances and open problems ⋮ Prequential analysis of complex data with adaptive model reselection ⋮ Intrinsic dimension of geometric data sets

Uses Software

• IntDim

Cites Work

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• Neural Network Learning
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• 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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