COMPARATIVE STUDY OF LOCAL FRACTAL ANALYSIS BY ALL PERMUTATIONS METHOD AND PAIRWISE EXPERT HISTOGRAMS COMPARISON ...
2016jgw | V.A. Panchelyuga, M.S. Panchelyuga, V.A. Kolombet, at all. // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics RAS, Pushchino, Russia; Chemical and Nuclear Engineering Department, Polytechnic University of Valencia, Spain, email@example.com
The paper deals with the comparative analysis of two methods for local analysis of
noise-like time series. One of the methods, a local fractal analysis by all permutations
combinations method (APM) [1, 2], has already proven its effectivity as an instrument
that allowed authors to reveal a stable frequency structure in time series of the ?-decay
rate fluctuations [3, 4]. The second one is a pairwise expert comparison of the smoothed
histogram shapes [1-2, 5]. The methods share a set of the properties: invariance under
linear transformations (shifts, dilatations, and mirror reflections), the same as invariance
with respect to rearrangement of terms in section of time series that bases calculations of
the APM dimensions and construction of a smoothed histogram. The analysis showed that
74% of the pairs selected fully automatically by the APM are the same that were selected
in course of expert pairwise histogram comparison, while 26% of the ACM selected pairs
were never selected by any expert.