Method of Distinguishing Styles by Fractal and Statistical Indicators of the Text as a Sequence of the Number of Letters in Its Words

Kaminskiy, Roman; Shakhovska, Nataliya; Kajanová, Jana; Kryvenchuk, Yurii

doi:10.3390/math9192410

Cited by 1 publication

(1 citation statement)

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“…The authors of the publication determine the Wavelet-based method as an accurate method. Although the R/S method is not the most accurate, nowadays it is actively applied in the analysis of fractal processes in various scientific fields due to its easy of use [16][17][18][19][20][21][22].…”

Section: Related Workmentioning

confidence: 99%

Methods for Mathematical Analysis of Simulated and Real Fractal Processes with Application in Cardiology

et al. 2022

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In the article, a comparative analysis is performed regarding the accuracy parameter in determining the degree of self-similarity of fractal processes between the following methods: Variance-Time plot, Rescaled Range (R/S), Wavelet-based, Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). To evaluate the methods, fractal processes based of Fractional Gaussian Noise were simulated and the dependence between the length of the simulated process and the degree of self-similarity was investigated by calculating the Hurst exponent (H > 0.5). It was found that the Wavelet-based, DFA and MFDFA methods, with a process length greater than 214 points, have a relative error of the Hurst exponent is less than 1%. A methodology for the Wavelet-based method related to determining the size of the scale and the wavelet algorithm was proposed, and it was investigated in terms of the exact determination of the Hurst exponent of two algorithms: Haar and Daubechies with different number of coefficients and different values of the scale. Based on the analysis, it was determined that the Daubechies algorithm with 10 coefficients and scale (i = 2, j = 10) has a relative error of less than 0.5%. The three most accurate methods are applied to the study of real cardiac signals of two groups of people: healthy and unhealthy (arrhythmia) subjects. The results of the statistical analysis, using the t-test, show that the proposed methods can distinguish the two studied groups and can be used for diagnostic purposes.

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