Fractal-Based Methods as a Technique for Estimating the Intrinsic Dimensionality of High-Dimensional Data: A Survey

Article type: Research Article

Authors: Karbauskaitė, Rasa^{; *} | Dzemyda, Gintautas

Affiliations: Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania. E-mails: rasa.karbauskaite@mii.vu.lt, gintautas.dzemyda@mii.vu.lt

Correspondence: [*] Corresponding author.

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.

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

Journal: Informatica, vol. 27, no. 2, pp. 257-281, 2016