Cross-correlations between signal's components

doi:10.1088/1674-1056/ad9ffb

中国物理B ›› 2025, Vol. 34 ›› Issue (2): 28702-028702.doi: 10.1088/1674-1056/ad9ffb

Cross-correlations between signal's components

Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰)†

Department of Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, China

收稿日期:2024-10-21 修回日期:2024-11-30 接受日期:2024-12-17 出版日期:2025-02-15 发布日期:2025-01-15
通讯作者: Huijie Yang E-mail:hjyang@ustc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11875042 and 11505114) and the Shanghai Project for Construction of Top Disciplines (Grant No. USST-SYS-01).

Cross-correlations between signal's components

Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰)†

Department of Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2024-10-21 Revised:2024-11-30 Accepted:2024-12-17 Online:2025-02-15 Published:2025-01-15
Contact: Huijie Yang E-mail:hjyang@ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11875042 and 11505114) and the Shanghai Project for Construction of Top Disciplines (Grant No. USST-SYS-01).

摘要/Abstract

摘要： Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix (network). Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory (RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only $7$ components from RESP (scattered in four sub-clusters) take part in the realization of coupling between the two signals.

关键词: coupling structure, cross-correlation matrix, component correlation network

Abstract: Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix (network). Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory (RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only $7$ components from RESP (scattered in four sub-clusters) take part in the realization of coupling between the two signals.

Key words: coupling structure, cross-correlation matrix, component correlation network

中图分类号: (Biological signal processing)

87.85.Ng

64.60.aq (Networks) 11.15.Me (Strong-coupling expansions)

Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰). Cross-correlations between signal's components[J]. 中国物理B, 2025, 34(2): 28702-028702.

Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰). Cross-correlations between signal's components[J]. Chin. Phys. B, 2025, 34(2): 28702-028702.

参考文献

[1] Gao Z K, Small M and Kurths J 2017 Europhys. Lett. 116 50001
[2] Hutchison R M, Womelsdorf T, Allen E A, Bandettini P A, Calhoun V D, Corbetta M, Della Penna S, Duyn J H, Glover G H, Gonzalez- Castillo J and Handwerker D A 2013 Neuroimage. 80 360
[3] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V and Sugihara G 2009 Nature 461 53
[4] Tirabassi G and Masoller C 2022 Chaos, Solitions and Fractals 155 111720
[5] Patro D K, Qi M and Sun X 2013 J. Fin. Stab. 9 105
[6] Dakos V, van Nes E and Scheffer M 2009 Nat. Preced. 1-1
[7] Ouyang F Y, Zheng B and Jiang X F 2019 Physica A 517 515
[8] Moon Y I, Rajagopalan B and Lall U 1995 Phys. Rev. E 52 2318
[9] Donges J F, Zou Y, Marwan N and Kurths J 2009 Eur. Phys. J. Spec. Top. 174 157
[10] Wu T, Gao X, An F and Kurths J 2023 Chaos, Solitions and Fractals 167 113052
[11] Lanford III O E and Ruelle D 1969 Commun. Math. Phys. 13 194
[12] Rangarajan G and Ding M 2000 Phys. Rev. E 61 4991
[13] Zhang M and Wang Y M 2020 Chin. Phys. B 29 048901
[14] Beenakker C W 1997 Rev. Mod. Phys. 69 731
[15] Edelman A and Rao N R 2005 Acta Numer. 14 233
[16] Tan L, Chen J J, Zheng B and Ouyang F Y 2016 PloS One 11 e0149648
[17] Ouyang F Y, Zheng B and Jiang X F 2014 Physica A 402 236
[18] Chen J J, Tan L and Zheng B 2015 Sci. Rep. 5 8399
[19] Zhou L, Qiu L, Gu C G and Yang H J 2018 Europhys. Lett. 121 48002
[20] Yan S, L S,Wang H Y, Gu C G and Yang H J 2022 Europhys. Lett. 138 61001
[21] Zou Y, Donner R V, Marvan N, Donges J F and Kurths J 2019 Phys. Rep. 787 1
[22] Zanin M, Papo D, Sousa P A, Menasalvas E, Nicchi A, Kubik E and Boccaletti S 2016 Phys. Rep. 635 1
[23] Park H J and Friston K 2013 Science 342 1238411
[24] Squartini T, Caldarelli G, Cimini G, Gabrielli A and Garlaschelli D 2018 Phys. Rep. 757 1
[25] Zhang J and Small M 2006 Phys. Rev. Lett. 96 238701
[26] Yang Y and Yang H J 2008 Physica A 387 1381
[27] Donner RV, Zou Y, Donges JF, Marwan N and Kurths J 2010 New J. Phys. 12 033025
[28] Lacasa L, Luque B, Ballesteros F, Luque J and Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 4972
[29] Luque B, Lacasa L, Ballesteros F and Luque J 2009 Phys. Rev. E 80 046103
[30] Ni X H, Jiang Z Q, Zhou W X 2009 Phys. Lett. A 373 3822
[31] Scarsoglio S, Laio F and Ridolfi L 2013 PloS One 8 e71129
[32] Donges JF, Zou Y, Marwan N and Kurths J 2009 Europhys. Lett. 87 48007
[33] Boers N, Goswami B, Rheinwalt A, Bookhagen B, Hoskins B and Kurths J 2019 Nature 566 373
[34] Friston K J 2011 Brain Connect. 1 13
[35] Bashan A, Bartsch R P, Kantelhardt JW, Havlin S and Ivanov P C 2012 Nat. Commun. 3 702
[36] Bartsch R P, Liu K K, Bashan A and Ivanov P C 2015 PloS One 10 e0142143
[37] Ma L, Chen M, He A, Cheng D and Yang X 2023 Chin. Phys. B 32 100501
[38] Buckner R L and DiNicola L M 2019 Nat. Rev. Neurosci. 20 593
[39] Liu K L, Bartsch R P, Ma Q D and Ivanov P C 2015 J. Phys. Conf. Ser. 640 012013
[40] Haluszczynski A, Laut I, Modest H and Rath C 2017 Phys. Rev. E 96 062315
[41] Tipton C 2022 Johnson Matthey Technol. Rev. 66 169
[42] Cooley J W and Tukey J W 1965 Math. Comput. 19 297
[43] Torrence C and Compo G P 1998 Bull. Am. Meteorol. Soc. 79 61
[44] Suarez D A and Salazar A 2009 Opt. Commun. 282 4203
[45] Xu X, Zhang J and Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[46] Tumminello M, Aste T, Di Matteo T and Mantegna R N 2005 Proc. Natl. Acad. Sci. USA 102 10421
[47] Zhang J, Luo X, Nakamura T, Sun J and Small M 2007 Phys. Rev. E 75 016218
[48] Donner R V, Small M, Donges J F, Marwan N, Zou Y, Xiang R X and Kurths J 2011 Int. J. Bifurcat. Chaos 21 1019
[49] Pimentel M A, Johnson A E, Charlton P H, Birrenkott D, Watkinson P J, Tarassenko L and Clifton D A 2016 IEEE T. Bio-Med. Eng. 64 1914
[50] Goldberger A L, Amaral L A, Glass L, Hausdorff J M, Ivanov P C, Mark R G and Stanley H E 2000 Circulation 101 e215
[51] Gao Z K and Jin N D 2009 Phys. Rev. E 79 066303
[52] McCullough M, Small M, Stemler T and Lu H H C 2015 Chaos 25 053101

Cross-correlations between signal's components

Cross-correlations between signal's components

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	朱世钊, 李信利, 聂森, 张文轻, 余高峰, 韩筱璞, 汪秉宏. Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis[J]. 中国物理B, 2015, 24(5): 58903-058903.
[2]	刘树波, 孙婧, 徐正全, 刘金硕. Digital chaotic sequence generator based on coupled chaotic systems[J]. 中国物理B, 2009, 18(12): 5219-5227.