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Complex networks are capable of modeling different kinds of complex systems in nature and technology, which contain a large number of components interacting with each other in a complicated manner. Quite recently, various approaches to analyzing time series by means of complex networks have been proposed, and their great potentials for uncovering valuable information embedded in time series, especially when nonlinear dynamical systems are incapable of being described by theoretical models have been proven. Despite the existing contributions, up to now, mapping time series into complex networks is still a challenging problem. In order to more effectively dig out the structural characteristics of time series (especially the nonlinear time series) and simplify the computational complexity of time series analysis, in this paper we present a novel method of constructing a directed weighted complex network based on time series symbolic pattern representation combined with sliding window technique. The proposed method firstly implements symbolic procession according to the equal probability segment division and then combines with the sliding window technique to determine the symbolic patterns at different times as nodes of the network. Next, the transition frequency and direction of symbolic patterns are set as the weights and directions of the network edges, thus establishing the directed weighted complex network of the analyzed time series. The results of test using the Logistic system with different parameter settings show that the topological structures of the directed weighted complex network can not only intuitively distinguish the periodic time series and chaotic time series, but also accurately reflect the subtle changes of two types of time series. These results are superior to those from the classical visibility graph method which can be only roughly classified as two types of signals. Finally, the proposed technique is used to investigate the natural wind field signals collected at an outdoor open space in which nine high precision two-dimensional (2D) ultrasonic anemometers are deployed in line with 1 m interval. The topological parameters of the network analysis include the network size, weighted clustering coefficient, and average path length. The corresponding results of our approach indicate that the values of three network parameters show consistent increase or decrease trend with the spatial regular arrangement of the nine anemometers. While the results of the visibility graph network parameters are irregular, and cannot accurately predict the spatial deployment relationship of nine 2D ultrasonic anemometers. These interesting findings suggest that topological features of the directed weighted complex network are potentially valuable characteristics of wind signals, which will have broad applications in researches such as wind power prediction, wind pattern classification and wind field dynamic analysis.
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Keywords:
- directed weighted complex network /
- time series analysis /
- visibility graph /
- Logistic system
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[2] Barabasi A L, Albert R 1999 Science 286 509
[3] Albert R, Barabsi A L 2002 Rev. Mod. Phys. 74 47
[4] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
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[7] Hao X, An H, Qi H, Gao X Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) [周磊, 龚志强, 支蓉, 封国林 2008 物理学报 57 7380]
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[13] Huang X, An H, Gao X 2015 Physica A 428 493
[14] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[15] Gao Z K, Fang P C, Ding M S, Jin N D 2015 Exp. Therm. Fluid Sci. 60 157
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[17] Yang Y, Yang H 2008 Physica A 387 1381
[18] Gao Z, Jin N 2009 Chaos 19 033137
[19] Tang J, Liu F, Zhang W, Zhang S, Wang Y 2016 Physica A 450 635
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[21] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 13
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[23] Liu C, Zhou W X, Yuan W K 2010 Physica A 389 2675
[24] Lin J, Keogh E, Lonardi S, Chiu B 2003 Proceedings of the 8th ACM SIGMOD workshop on Research Issues in Data Mining and Knowledge Discovery San Diego, USA, June 13, 2003 p2
[25] Lin J, Keogh E, Li W, Lonardi S 2007 Data Mining and Knowledge Discovery 15 107
[26] L J H, Lu J A, Chen S H 2001 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) p12 (in Chinese) [吕金虎, 陆君安, 陈士华 2001 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第12页]
[27] Shirazi A H, Jafari G R, Davoudi J, Peinke J, Tabar M R R, Sahimi M 2009 J. Statist. Mech.: Theory and Experiment 2009 P07046
[28] Antoniou I E, Tsompa E T 2008 Discrete Dyn. Nat. Soc. 2008 1
[29] Li J G, Meng Q H, Wang Y, Zeng M 2011 Autonomous Robots 30 281
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabasi A L, Albert R 1999 Science 286 509
[3] Albert R, Barabsi A L 2002 Rev. Mod. Phys. 74 47
[4] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[5] Rubinov M, Sporns O 2010 Neuroimage 52 1059
[6] Zhuang E, Small M, Feng G 2014 Physica A 410 483
[7] Hao X, An H, Qi H, Gao X Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) [周磊, 龚志强, 支蓉, 封国林 2008 物理学报 57 7380]
[8] Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys.Sin. 57 7380 (in Chinese) [周磊, 龚志强, 支蓉, 封国林 2008 物理学报 57 7380]
[9] Lacasa L, Toral R 2010 Phys. Rev. E 82 036120
[10] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[11] Donges J F, Donner R V, Kurths J 2013 Europhys. Lett. 102 10004
[12] Zou Y, Small M, Liu Z 2014 New J. Phys. 16 013051
[13] Huang X, An H, Gao X 2015 Physica A 428 493
[14] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[15] Gao Z K, Fang P C, Ding M S, Jin N D 2015 Exp. Therm. Fluid Sci. 60 157
[16] Takens F 1981 Dynamical Systems and Turbulence, Warwick 1980 898 366
[17] Yang Y, Yang H 2008 Physica A 387 1381
[18] Gao Z, Jin N 2009 Chaos 19 033137
[19] Tang J, Liu F, Zhang W, Zhang S, Wang Y 2016 Physica A 450 635
[20] Webber C L, Zbilut J P 1994 J. Appl. Phys. 76 965
[21] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 13
[22] Gao Z K, Hu L D, Zhou T T, Jin N D 2013 Acta Phys. Sin. 62 110507 (in Chinese) [高忠科, 胡沥丹, 周婷婷, 金宁德 2013 物理学报 62 110507]
[23] Liu C, Zhou W X, Yuan W K 2010 Physica A 389 2675
[24] Lin J, Keogh E, Lonardi S, Chiu B 2003 Proceedings of the 8th ACM SIGMOD workshop on Research Issues in Data Mining and Knowledge Discovery San Diego, USA, June 13, 2003 p2
[25] Lin J, Keogh E, Li W, Lonardi S 2007 Data Mining and Knowledge Discovery 15 107
[26] L J H, Lu J A, Chen S H 2001 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) p12 (in Chinese) [吕金虎, 陆君安, 陈士华 2001 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第12页]
[27] Shirazi A H, Jafari G R, Davoudi J, Peinke J, Tabar M R R, Sahimi M 2009 J. Statist. Mech.: Theory and Experiment 2009 P07046
[28] Antoniou I E, Tsompa E T 2008 Discrete Dyn. Nat. Soc. 2008 1
[29] Li J G, Meng Q H, Wang Y, Zeng M 2011 Autonomous Robots 30 281
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