摘要The multiscale entropy (MSE) reveals the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. However, most research results are pure experimental search. Recently, Costa et al. have made the first attempt to present the theoretical basis of MSE, but it only supports the Gaussian distribution [Phys Rev. E 71 (2005) 021906]. We present the theoretical basis of MSE under the inverse Gaussian distribution, a typical model for physiological, physical and financial data sets. The analysis allows for ncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, and then provides a reliable foundation for the potential applications of MSE to explore complex physical and physical time series.
Abstract：The multiscale entropy (MSE) reveals the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. However, most research results are pure experimental search. Recently, Costa et al. have made the first attempt to present the theoretical basis of MSE, but it only supports the Gaussian distribution [Phys Rev. E 71 (2005) 021906]. We present the theoretical basis of MSE under the inverse Gaussian distribution, a typical model for physiological, physical and financial data sets. The analysis allows for ncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, and then provides a reliable foundation for the potential applications of MSE to explore complex physical and physical time series.
[1] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297 [2] Richman J S and Moorman J R 2000 Am. J. Physiol. 278H2039 [3] Lin J and Ning X B 2005 Chin. Sci. Bull. 50 1269 [4] Costa M, Goldberger A L and Peng C K 2002 Phys. Rev. Lett. 89 068102 [5] Costa M et al %, Goldberger A L and Peng C K2005 Phys. Rev. E 71 021906 [6] Thuraisingham R A and Gottwald G A 2006 Physica A 366 323 [7] Markowiec D Galaska R, Dudkowska A, Rynkiewicz A and Zwierz M 2006 Physica A 369 632 [8] Ferrario M, Signorini M G, Magenes G and Cerutti S 2006 IEEE Trans. Biomedical Engin. 53 119 [9] Costa M, Goldberger A L and Peng C K 2005 Phys. Rev.Lett. 95 198102 [10] Ilow J and Hatzinakos D 1998 IEEE Trans. Signal Proc. 46 1601 [11] Iyengar S and Liao Q 1997 Biol. Cybem. 77 289 [12] Barbieri R et al %, Matten E C, Alabi A A, and.Brown E N2005 Am. J.Physiol. 288 H424 [13] Sun Z et al %, He D, Liang L and Cruickshank H2004 IEE Proc.Softw. 151 248 [14] Kamstra M and Milevsky M A 2005 Quantitative Finance 5 3 237 [15] Folks J L and Chhikara R S 1978 J. R. Statist. Soc.London B 40 263 [16] Ninness B 1998 IEEE Trans. Inform. Theor. 44 1 32 [17] Barndorff-Nielsen O E et al 1991 Canadian J. Statist. 20 209 [18] Minami M 2003 Commun. Statist. 32 2285 [19] Bao J D, Huang H Y and Jia Y 2005 Phys. Rev. E 72051105 [20] Bao J D 2005 Prog. Phys. 25 359 (in Chinese)
2007, Vol. 24 
