{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:44:32Z","timestamp":1760784272022,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T00:00:00Z","timestamp":1494806400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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     ( q ,  q \u2032  )    -entropy is a wavelet-based extension of the     ( q ,  q \u2032  )    -entropy of Borges and is based on the entropy planes for various q and     q \u2032    ; it is theoretically shown that it constitutes an efficient and effective technique for fractal signal classification. Moreover, the second parameter     q \u2032     provides further analysis flexibility and robustness in the sense that different     ( q ,  q \u2032  )     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.<\/jats:p>","DOI":"10.3390\/e19050224","type":"journal-article","created":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T12:16:12Z","timestamp":1494850572000},"page":"224","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0397-6063","authenticated-orcid":false,"given":"Julio","family":"Ram\u00edrez-Pacheco","sequence":"first","affiliation":[{"name":"Department of Basic Sciences and Engineering, DCBeI, University of Caribe, SM-78, Mza-1, Lote-1, Esquina Fraccionamiento Tabachines, 77528 Canc\u00fan, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9326-7713","authenticated-orcid":false,"given":"Joel","family":"Trejo-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"CONACYT-Centro de Investigaci\u00f3n en Matem\u00e1ticas, Carretera Sierra Papacal, Chuburna Puerto km 5, 97302 M\u00e9rida, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joaquin","family":"Cortez-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Instituto Tecnol\u00f3gico de Sonora, 5 de Febrero, 818 Sur, Colonia Centro, 85000 Ciudad Obreg\u00f3n, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ram\u00f3n","family":"Palacio","sequence":"additional","affiliation":[{"name":"Unidad Navojoa, Instituto Tecnol\u00f3gico de Sonora, Ram\u00f3n Corona y Aguacalientes S\/N, Col. ITSON, 85860 Navojoa, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.physa.2014.10.073","article-title":"Long-range correlations and trends in Colombian seismic time series","volume":"421","author":"Quimbary","year":"2015","journal-title":"Physica A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.dsp.2014.11.007","article-title":"Application of a time-scale local Hurst exponent analysis to time series","volume":"37","year":"2015","journal-title":"Digit. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1037\/0096-3445.134.1.117","article-title":"Human cognition and 1\/f scaling","volume":"134","author":"Holden","year":"2005","journal-title":"J. Exp. Psychol. 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