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Sample entropy or approximate entropy, a complexity measure that quantifies the new information generation rate and is applicable to short time series, has been widely applied to physiological signal analysis since it was proposed. However, on one hand, sample entropy is easily affected by non-stationary sudden noise, because the tolerance during calculation is set to be proportional to standard deviation; on the other hand, it is not independent of the probability distribution, so that it does not purely characterize the new information generation rate. To solve these two problems, a new improved method named equiprobable symbolization sample entropy is proposed in this paper. Through equiprobable symbolization, the effects of both non-stationary sudden noises and probability distribution are eliminated. Besides, since equiprobable symbolization is usually non-uniform, it further breaks through the linear constrains in classic sample entropy. The method is proved to be rational by simulating three typical noises that have different time correlations and new information generation rates. Then the method is applied to electroencephalography (EEG) analysis. Results show that the method can successfully discriminate two different attention levels based on EEG with duration as short as 1.25 s and without removing any artificial artifacts. Therefore, the method is of great significance for EEG biofeedback, in which strong real-time abilities are usually required.
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Keywords:
- symbolic dynamics /
- equiprobable symbolization /
- sample entropy /
- electroencephalography biofeedback
[1] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[2] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart Circ. Physiol. 278 2039
[3] Bruhn J, Röpcke H, Hoeft A 2000 Anesthesiology 92 715
[4] Lake D E, Richman J S, Griffin M P, Moorman J R 2002 Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 R789
[5] Srinivasan V, Eswaran C, Sriraam N 2007 IEEE Trans. Inf. Technol. Biomed. 11 288
[6] Sohn H, Kim I, Lee W, Peterson B S, Hong H, Chae J H, Hong S, Jeong J 2010 Clin. Neurophysiol. 121 1863
[7] Acharya U R, Molinari F, Sree S V, Chattopadhyay S, Ng K H, Suri J S 2012 Biomed. Signal Proces. Control. 7 401
[8] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[9] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[10] Hu M, Liang H 2012 IEEE Trans. Biomed. Eng. 59 12
[11] Song A L, Huang X L, Si J F, Ning X B 2011 Acta Phys. Sin. 60 020509 (in Chinese) [宋爱玲, 黄晓林, 司峻峰, 宁新宝 2011 物理学报 60 020509]
[12] Zhang M, Wang J 2013 Acta Phys. Sin. 62 038701 (in Chinese) [张梅, 王俊 2013 物理学报 62 038701]
[13] Wu S, Li J, Zhang M L, Wang J 2013 Acta Phys. Sin. 62 238701 (in Chinese) [吴莎, 李锦, 张明丽, 王俊 2013 物理学报 62 238701]
[14] Chen G, Xie L, Chu J 2013 Chin. Phys. B 22 038902
[15] Wang J, Yu Z F 2012 Chin. Phys. B 21 018702
[16] Lin J, Keogh E, Wei L, Lonardi S 2007 Data Min. Knowl. Disc. 15 107
[17] Hou F Z, Huang X L, Chen Y, Huo C Y, Liu H X, Ning X B 2013 Phys. Rev. E 87 012908
[18] Kantz H, Schreiber T 2003 Nonlinear Time Series Analysis (2nd Ed.) (Cambridge: Cambridge University Press) pp39-40
[19] Klimesch W 1999 Brain Res. Rev. 29 169
[20] David J V 2005 Appl. Psychophysiol. Biofeedback 30 347
[21] Egner T, Gruzelier J H 2004 Clin. Neurophysiol. 115 131
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[1] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[2] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart Circ. Physiol. 278 2039
[3] Bruhn J, Röpcke H, Hoeft A 2000 Anesthesiology 92 715
[4] Lake D E, Richman J S, Griffin M P, Moorman J R 2002 Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 R789
[5] Srinivasan V, Eswaran C, Sriraam N 2007 IEEE Trans. Inf. Technol. Biomed. 11 288
[6] Sohn H, Kim I, Lee W, Peterson B S, Hong H, Chae J H, Hong S, Jeong J 2010 Clin. Neurophysiol. 121 1863
[7] Acharya U R, Molinari F, Sree S V, Chattopadhyay S, Ng K H, Suri J S 2012 Biomed. Signal Proces. Control. 7 401
[8] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[9] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[10] Hu M, Liang H 2012 IEEE Trans. Biomed. Eng. 59 12
[11] Song A L, Huang X L, Si J F, Ning X B 2011 Acta Phys. Sin. 60 020509 (in Chinese) [宋爱玲, 黄晓林, 司峻峰, 宁新宝 2011 物理学报 60 020509]
[12] Zhang M, Wang J 2013 Acta Phys. Sin. 62 038701 (in Chinese) [张梅, 王俊 2013 物理学报 62 038701]
[13] Wu S, Li J, Zhang M L, Wang J 2013 Acta Phys. Sin. 62 238701 (in Chinese) [吴莎, 李锦, 张明丽, 王俊 2013 物理学报 62 238701]
[14] Chen G, Xie L, Chu J 2013 Chin. Phys. B 22 038902
[15] Wang J, Yu Z F 2012 Chin. Phys. B 21 018702
[16] Lin J, Keogh E, Wei L, Lonardi S 2007 Data Min. Knowl. Disc. 15 107
[17] Hou F Z, Huang X L, Chen Y, Huo C Y, Liu H X, Ning X B 2013 Phys. Rev. E 87 012908
[18] Kantz H, Schreiber T 2003 Nonlinear Time Series Analysis (2nd Ed.) (Cambridge: Cambridge University Press) pp39-40
[19] Klimesch W 1999 Brain Res. Rev. 29 169
[20] David J V 2005 Appl. Psychophysiol. Biofeedback 30 347
[21] Egner T, Gruzelier J H 2004 Clin. Neurophysiol. 115 131
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