Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy
Department of Basic Sciences and Engineering, DCBeI, University of Caribe, SM-78, Mza-1, Lote-1, Esquina Fraccionamiento Tabachines, 77528 Cancún, Mexico
CONACYT-Centro de Investigación en Matemáticas, Carretera Sierra Papacal, Chuburna Puerto km 5, 97302 Mérida, Mexico
Department of Electrical Engineering, Instituto Tecnológico de Sonora, 5 de Febrero, 818 Sur, Colonia Centro, 85000 Ciudad Obregón, Mexico
Unidad Navojoa, Instituto Tecnológico de Sonora, Ramón Corona y Aguacalientes S/N, Col. ITSON, 85860 Navojoa, Mexico
Author to whom correspondence should be addressed.
Academic Editor: Carlo Cattani
Received: 3 March 2017 / Revised: 28 April 2017 / Accepted: 9 May 2017 / Published: 15 May 2017
This article proposes a methodology for the classification of fractal signals as stationary or nonstationary. The methodology is based on the theoretical behavior of two-parameter wavelet entropy of fractal signals. The wavelet
-entropy is a wavelet-based extension of the
-entropy of Borges and is based on the entropy planes for various q
; it is theoretically shown that it constitutes an efficient and effective technique for fractal signal classification. Moreover, the second parameter
provides further analysis flexibility and robustness in the sense that different
pairs can analyze the same phenomena and increase the range of dispersion of entropies. A comparison study against the standard signal summation conversion technique shows that the proposed methodology is not only comparable in accuracy but also more computationally efficient. The application of the proposed methodology to physiological and financial time series is also presented along with the classification of these as stationary or nonstationary.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Ramírez-Pacheco, J.C.; Trejo-Sánchez, J.A.; Cortez-González, J.; Palacio, R.R. Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy. Entropy 2017, 19, 224.
Ramírez-Pacheco JC, Trejo-Sánchez JA, Cortez-González J, Palacio RR. Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy. Entropy. 2017; 19(5):224.
Ramírez-Pacheco, Julio C.; Trejo-Sánchez, Joel A.; Cortez-González, Joaquin; Palacio, Ramón R. 2017. "Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy." Entropy 19, no. 5: 224.
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