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Low Bias Local Intrinsic Dimension Estimation from Expected Simplex Skewness

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Author

  • Kerstin Johnsson
  • Charlotte Soneson
  • Magnus Fontes

Summary, in English

In exploratory high-dimensional data analysis, local intrinsic dimension estimation can sometimes be used in order to discriminate between data sets sampled from different low-dimensional structures. Global intrinsic dimension estimators can in many cases be adapted to local estimation, but this leads to problems with high negative bias or high variance. We introduce a method that exploits the curse/blessing of dimensionality and produces local intrinsic dimension estimators that have very low bias, even in cases where the intrinsic dimension is higher than the number of data points, in combination with relatively low variance. We show that our estimators have a very good ability to classify local data sets by their dimension compared to other local intrinsic dimension estimators; furthermore we provide examples showing the usefulness of local intrinsic dimension estimation in general and our method in particular for stratification of real data sets.

Publishing year

2015

Language

English

Pages

196-202

Publication/Series

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volume

37

Issue

1

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics

Keywords

  • Eigenvalues and eigenfunctions
  • Calibration
  • Estimation
  • Dimension
  • Manifolds

Status

Published

ISBN/ISSN/Other

  • ISSN: 1939-3539