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A traffic flow time series is a sequence of traffic detection parameters in chronological order. This differs from a general quantitative data sequence in that the time series includes a time attribute that contains not only the data with time characteristics, but also the distribution of the data itself. To date, studies of traffic time series have primarily adopted data mining methods consisting of data mining and machine learning methods–similar sequence search, dimension reduction, clustering, classification, pattern analysis, prediction, etc. In order to improve the visualization of traffic flow time series and feature analyses, a proposed method builds the association networks of traffic flow time series by using visibility graph theory. This approach differs from traditional traffic flow theory as it performs feature analysis of traffic flow time series from the perspective of complex networks, and then analyzes the relationship between the characteristics of the structure in the visual network and the state characteristics of the traffic flow. The proposed method also takes into account the different traffic flow time sequences that correspond to different traffic states.In the network building process using the proposed method, the traffic flow is classified by correlating the traffic flow parameters to the structure of the complex time series networks under different traffic conditions through considering the changes in traffic flow characteristics under various traffic conditions. Next, statistical analyses of the signs and attributes of the networks (e.g. degree distribution, clustering coefficient, network diameter, and modularization) are conducted. The analysis results show that the proposed visibility graph method can provide an effective approach to mapping traffic flow time series to the network. Moreover, the modularity, clustering coefficient, and degree distribution of the traffic flow time series networks in different traffic states show specifically varying patterns, providing a way to visually analyze the trends in traffic flow operation. When the traffic condition is at level 1, the distribution of the scattered points of the network conforms to a power law distribution. When the traffic condition is at any other level, the distribution of the scattered points of the network is consistent with a Gaussian distribution. The modularity of the time series network also shows some statistical characteristics, that is, the number of modules grows rapidly when the traffic state switches from smooth to moderate congestion, but decreases slowly when the traffic state switches from moderate congestion to serious congestion. These characteristics can be used to distinguish different traffic states, providing more perspective to understand different traffic scenarios. In this work we preliminarily study the attributes of traffic time series based on the proposed visibility graph method. Future efforts will continue to compare various methods of time series network construction to determine the pros and cons of each method for further analysis.
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Keywords:
- traffic flow time series /
- visibility graph /
- complex network /
- cluster
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[16] Zhang J, Sun J F, Luo X D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[17] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[18] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. 105 19601
[19] Donner R V, Zou Y, Donges J F, Marwan N, Kurths J 2010 Phys. Rev. E 81 15101
[20] Yang Y, Yang H J 2008 Physica A 387 1381
[21] Tang J, Wang Y, Liu F 2013 Physica A 392 4192
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[1] He Z C, Li Z T, Zhao J M 2010 J. Sw. Jiaotong Univ. 45 946 (in Chinese)[何兆成, 黎志涛, 赵建明 2010 西南交通大学学报 45 946]
[2] Dou H L, Liu H D, Wu Z Z, Yang X G 2009 J. Tongji Univ. (Natural Science Edition) 37 486 (in Chinese)[窦慧丽, 刘好德, 吴志周, 杨晓光 2009 同济大学学报(自然科学版) 37 486]
[3] Xing X, Yu D X, Tian X J, Cheng Z Y 2016 J. Huazhong Univ. Sci. Technol. (Natural Science Edition) 44 160808 (in Chinese)[邢雪, 于德新, 田秀娟, 程泽阳 2016 华中科技大学学报(自然科学版) 44 160808]
[4] Zhang Y M, Wu X J, Bai S L 2013 Acta Phys. Sin. 62 190509 (in Chinese)[张玉梅, 吴晓军, 白树林 2013 62 190509]
[5] Treiber M, Kesting A, Helbing D 2010 Transp. Res. B 44 983
[6] Ling X, Hu M B, Jiang R, Wu Q S 2010 Phys. Rev. E 81 16113
[7] Gao Z K, Jin N D, Yang D, Zhai L S, Du M 2012 Acta Phys. Sin. 61 120510 (in Chinese)[高忠科, 金宁德, 杨丹, 翟路生, 杜萌 2012 61 120510]
[8] Gao X Y, An H Z, Fang W 2012 Acta Phys. Sin. 61 098902 (in Chinese)[高湘昀, 安海忠, 方伟 2012 61 098902]
[9] Gao Z, Jin N 2012 Physica A 391 3005
[10] Zhang J, Cao X B, Du W B, Cai K Q 2010 Physica A 389 3922
[11] Arora P, Deepali D, Varshney S 2016 Proc. Comput. Sci. 78 507
[12] Madhulatha T 2012 Int. Organ. Sci. Res. J. Eng. 2 719
[13] Mishra N, Motwani R 2004 Mach. Learn. 56 35
[14] Lucas L, Bartolo L, Fernando B, Jordi L, Juan C N 2008 Proc. Natl. Acad. Sci. 105 4972
[15] Lacasa L, Toral R 2010 Phys. Rev. E 82 36120
[16] Zhang J, Sun J F, Luo X D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[17] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[18] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. 105 19601
[19] Donner R V, Zou Y, Donges J F, Marwan N, Kurths J 2010 Phys. Rev. E 81 15101
[20] Yang Y, Yang H J 2008 Physica A 387 1381
[21] Tang J, Wang Y, Liu F 2013 Physica A 392 4192
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