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Multiscale multivariate sample entropy can test the multivariate complexity, which is accepted as a kind of reflection of nonlinear dynamical interactions in multichannel data. It is however relatively unstable due to the rigid ranking scheme used in comparison among different patterns. It is not applicable to the nonlinear and non-stationary data because the multiscale framework used is in fact handled by moving average succeeded by down-sampling, which actually has a premise of stationary data. We substitute a fuzzy membership function for the original rigid one and compare the performances of different kinds of fuzzy membership functions. In addition, we employ the multivariate empirical mode decomposition (MEMD) to capture different scales. Results show that the substitution of fuzzy membership function brings in significant stability. It is much more obvious by using the introduced physical fuzzy membership function (PFMF). Also MEMD could capture scales more robustly. In conclusion, the introduced PFMF- and MEMD-based MMFE perform best. Final analysis on the interactions between heart rate variability (HRV) and heart diastolic time interval variability (DIV) validates it. In addition, the results show that the multivariate complexity between HRV and DIV decreases in aging or heart failure group but in a distinctly different decreasing manner–it deceased at low scales with aging, indicating a loss of short-range correlation but both at low and high scales with heart failure, which shows the losses of both short- and long-range correlations. Studies in noninvasive detection of cardiovascular diseases should benefit from the above conclusions.
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Keywords:
- multivariate complexity /
- multiscale multivariate fuzzy entropy /
- physical fuzzy membership function /
- multivariate empirical mode decomposition
[1] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[2] Pincus S M 1991 Proc. Nat. Acad. Sci. U.S.A. 88 2297
[3] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart. Circ. Physiol. 278 H2039
[4] Cao L, Mees A, Judd K 1998 Physica D 121 75
[5] Costa M, Goldberger A L, Peng C K 2002 Phys. Rev. Lett. 89 068102
[6] Ahmed M U, Li L, Cao J, Mandic D P 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Boston, Massachusetts, USA, Aug. 30-Sep. 3, 2011 p810
[7] Ahmed M U, Mandic D P 2012 IEEE Signal Process Lett. 19 91
[8] Looney D, Ahmed M U, Mandic D P 2012 Natural Intelligence: the INNS Magazine 1 40
[9] Li P, Liu C Y, Wang X P, Li L P, Yang L, Chen Y C, Liu C C 2013 Med. Biol. Eng. Comput. 58 581
[10] Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Med. Eng. Phys. 31 61
[11] Xiong G L, Zhang L, Liu H S, Zou H J, Guo W Z 2010 J. Zhejiang University-Science A 11 270
[12] Chen X J, Li Z, Bai B M, Pan W, Chen Q H 2011 J. Electron. Inform. Tech. 33 1198 (in Chinese) [陈小军, 李赞, 白宝明, 潘玮, 陈清华 2011 电子与信息学报 33 1198]
[13] Sun K H, He S B, Yin L Z, A D L·Duo L K 2012 Acta Phys. Sin. 61 130507 (in Chinese) [孙克辉, 贺少波, 尹林子, 阿地力·多力坤 2012 物理学报 61 130507]
[14] Liu C Y, Li K, Zhao L N, Liu F, Zheng D C, Liu C C, Liu S T 2013 Comput. Biol. Med. 43 100
[15] Nikulin V V, Brismar T 2004 Phys. Rev. Lett. 92 089803
[16] Valencia J F, Porta A, Vallverdu M, Claria F, Baranowski R, Orlowska-Baranowska E, Caminal P 2009 IEEE Trans. Biomed. Eng. 56 2202
[17] Huang N E, Shen Z, Long S R, Wu M C, Shih H H, Zheng Q, Yen N C, Tung C C, Liu H H 1998 Proc. R. Soc. London A 454 903
[18] Amoud H, Snoussi H, Hewson D, Doussot M, Duchene J 2007 IEEE Signal Process Lett. 14 297
[19] Rehman N, Mandic D P 2010 Proc. R. Soc. London, Ser. A 466 1291
[20] Hu M, Liang H 2012 IEEE Trans. Biomed. Eng. 59 12
[21] Ahmed M U, Rehman N, Looney D, Rutkowski T M, Mandic D P 2012 Bull. Pol. Ac.: Tech. 60 433
[22] Lu S, Chen X, Kanters J K, Solomon I C, Chon K H 2008 IEEE Trans. Biomed. Eng. 55 1966
[23] Liu C Y, Liu C C, Shao P, Li L P, Sun X, Wang X P, Liu F 2011 Physiol. Meas. 32 167
[24] Kaplan D T, Furman M I, Pincus S M, Ryan S M, Lipsitz L A, Goldberger A L 1991 Biophys. J. 59 945
[25] Iyengar N, Peng C K, Morin R, Goldberger A L, Lipsitz L A 1996 Am. J. Physiol. Regulatory Integrative Comp. Physiol. 271 R1078
[26] Liu C Y, Liu C C, Li L P, Zhang Q G, Li B 2009 3rd International Conference on Bioinformatics and Biomedical Engineering Beijing, China, June 11-13, 2009 p2609
[27] Li P, Liu C C, Zhang M, Che W B, Li J 2011 Acta Biophys. Sin. 27 222 (in Chinese) [李鹏, 刘常春, 张明, 车文彪, 李键 2011 生物物理学报 27 222]
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[1] Ahmed M U, Mandic D P 2011 Phys. Rev. E 84 061918
[2] Pincus S M 1991 Proc. Nat. Acad. Sci. U.S.A. 88 2297
[3] Richman J S, Moorman J R 2000 Am. J. Physiol. Heart. Circ. Physiol. 278 H2039
[4] Cao L, Mees A, Judd K 1998 Physica D 121 75
[5] Costa M, Goldberger A L, Peng C K 2002 Phys. Rev. Lett. 89 068102
[6] Ahmed M U, Li L, Cao J, Mandic D P 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society Boston, Massachusetts, USA, Aug. 30-Sep. 3, 2011 p810
[7] Ahmed M U, Mandic D P 2012 IEEE Signal Process Lett. 19 91
[8] Looney D, Ahmed M U, Mandic D P 2012 Natural Intelligence: the INNS Magazine 1 40
[9] Li P, Liu C Y, Wang X P, Li L P, Yang L, Chen Y C, Liu C C 2013 Med. Biol. Eng. Comput. 58 581
[10] Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Med. Eng. Phys. 31 61
[11] Xiong G L, Zhang L, Liu H S, Zou H J, Guo W Z 2010 J. Zhejiang University-Science A 11 270
[12] Chen X J, Li Z, Bai B M, Pan W, Chen Q H 2011 J. Electron. Inform. Tech. 33 1198 (in Chinese) [陈小军, 李赞, 白宝明, 潘玮, 陈清华 2011 电子与信息学报 33 1198]
[13] Sun K H, He S B, Yin L Z, A D L·Duo L K 2012 Acta Phys. Sin. 61 130507 (in Chinese) [孙克辉, 贺少波, 尹林子, 阿地力·多力坤 2012 物理学报 61 130507]
[14] Liu C Y, Li K, Zhao L N, Liu F, Zheng D C, Liu C C, Liu S T 2013 Comput. Biol. Med. 43 100
[15] Nikulin V V, Brismar T 2004 Phys. Rev. Lett. 92 089803
[16] Valencia J F, Porta A, Vallverdu M, Claria F, Baranowski R, Orlowska-Baranowska E, Caminal P 2009 IEEE Trans. Biomed. Eng. 56 2202
[17] Huang N E, Shen Z, Long S R, Wu M C, Shih H H, Zheng Q, Yen N C, Tung C C, Liu H H 1998 Proc. R. Soc. London A 454 903
[18] Amoud H, Snoussi H, Hewson D, Doussot M, Duchene J 2007 IEEE Signal Process Lett. 14 297
[19] Rehman N, Mandic D P 2010 Proc. R. Soc. London, Ser. A 466 1291
[20] Hu M, Liang H 2012 IEEE Trans. Biomed. Eng. 59 12
[21] Ahmed M U, Rehman N, Looney D, Rutkowski T M, Mandic D P 2012 Bull. Pol. Ac.: Tech. 60 433
[22] Lu S, Chen X, Kanters J K, Solomon I C, Chon K H 2008 IEEE Trans. Biomed. Eng. 55 1966
[23] Liu C Y, Liu C C, Shao P, Li L P, Sun X, Wang X P, Liu F 2011 Physiol. Meas. 32 167
[24] Kaplan D T, Furman M I, Pincus S M, Ryan S M, Lipsitz L A, Goldberger A L 1991 Biophys. J. 59 945
[25] Iyengar N, Peng C K, Morin R, Goldberger A L, Lipsitz L A 1996 Am. J. Physiol. Regulatory Integrative Comp. Physiol. 271 R1078
[26] Liu C Y, Liu C C, Li L P, Zhang Q G, Li B 2009 3rd International Conference on Bioinformatics and Biomedical Engineering Beijing, China, June 11-13, 2009 p2609
[27] Li P, Liu C C, Zhang M, Che W B, Li J 2011 Acta Biophys. Sin. 27 222 (in Chinese) [李鹏, 刘常春, 张明, 车文彪, 李键 2011 生物物理学报 27 222]
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