Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy

Abstract

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 ′ ) -entropy is a wavelet-based extension of the ( q , q ′ ) -entropy of Borges and is based on the entropy planes for various q and q ′ ; it is theoretically shown that it constitutes an efficient and effective technique for fractal signal classification. Moreover, the second parameter q ′ provides further analysis flexibility and robustness in the sense that different ( q , q ′ ) 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