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
Pub. online: 1 January 2016
Type: Research Article
Received
1 December 2015
1 December 2015
Accepted
1 April 2016
1 April 2016
Published
1 January 2016
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.