Translation and rotation invariant method of Renyi dimension estimation. (September 2018)

• Record Type: Journal Article
• Authors: Dlask, Martin; Kukal, Jaromir
• Is Part Of: Chaos, solitons and fractals. Volume 114(2018)
• Page Start: 536
• Page End: 541
• Publication Date: 2018-09
• Subjects: Parzen estimate -- Renyi entropy -- Monte carlo -- Renyi dimension; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.07.030
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: novel method of correlation dimension estimation based on Parzen estimate modified Renyi entropy as a translational and rotation invariant measure theoretically and numerically proven relationship to correlation dimension efficiency proved on the fractal sets with known dimension Abstract: A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented, and for the analysis of correlation dimension, a novel approach that employs the log-linear dependence of a modified Renyi entropy is used. The new formula for the Renyi entropy has been investigated both theoretically and experimentally on selected fractal sets.