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Fractal-Based Methods as a Technique for Estimating the Intrinsic Dimensionality of High-Dimensional Data: A Survey
Volume 27, Issue 2 (2016), pp. 257–281
Rasa Karbauskaitė   Gintautas Dzemyda  

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https://doi.org/10.15388/Informatica.2016.84
Pub. online: 1 January 2016      Type: Research Article     

Received
1 December 2015
Accepted
1 April 2016
Published
1 January 2016

Abstract

The estimation of intrinsic dimensionality of high-dimensional data still remains a challenging issue. Various approaches to interpret and estimate the intrinsic dimensionality are developed. Referring to the following two classifications of estimators of the intrinsic dimensionality – local/global estimators and projection techniques/geometric approaches – we focus on the fractal-based methods that are assigned to the global estimators and geometric approaches. The computational aspects of estimating the intrinsic dimensionality of high-dimensional data are the core issue in this paper. The advantages and disadvantages of the fractal-based methods are disclosed and applications of these methods are presented briefly.

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Vilnius University

Keywords
high-dimensional data intrinsic dimensionality topological dimension fractal dimension fractal-based methods box-counting dimension information dimension correlation dimension packing dimension

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INFORMATICA

  • Online ISSN: 1822-8844
  • Print ISSN: 0868-4952
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