Translation and rotation invariant method of Renyi dimension estimation

Martin Dlask and Jaromir Kukal

Chaos, Solitons & Fractals, 2018, vol. 114, issue C, 536-541

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.

Keywords: Parzen estimate; Renyi entropy; Monte carlo; Renyi dimension (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:114:y:2018:i:c:p:536-541

DOI: 10.1016/j.chaos.2018.07.030

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