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Analysis of urban human mobility behavior based on random matrix theory

Analysis of urban human mobility behavior based on random matrix theory

Xu Zan-Xin, Wang Yue, Si Hong-Bo, Feng Zhen-Ming
• Abstract

Mobile communication applications provide a unique data source for the research of human mobility pattern. Based on the distribution data of urban mobile phone users, in this paper is explored the macroscopic dynamical behavior of urban mobility human by using the method of random matrix theory. The largest eigenvalue and the corresponding eigenvector of mobile phone user data deviate far from the distribution of random matrix. The deviations from random matrix vary with time. We find that the largest eigenvalue corresponds to a whole behavior common to all urban human mobility. The results indicate the temporal trends of the mean of correlation coefficient and the largest eigenvalue. We also find that the spatio temporal evolution of the weight of eigenvector components for the eigenvector corresponding to the largest eigenvalue is very consistent with the fluctuation pattern of the macroscopic behavior of urban human mobility.

• Funds:

References

 [1] Bohannon J 2006 Science 314 914 [2] Onnela J O, Saramaki J, Hyvonen J, Szabo G, Lazer D, Kaski K, Kertesz J, Barabasi A L 2007 PNAS 104 18 [3] Marta C G, Cesar A H, Barabasi A L 2008 Nature 453 7196 [4] Hong W, Han X P, Zhou T, Wang B H 2009 Chinese Phys. Lett. 26 2 [5] Ratti C, Williams S, Frenchman D, Pulselli R M 2006 EPB 33 5 [6] Reades J, Calabrese F, Sevtsuk A, Ratti C 2007 IEEE Pervas Comput 6 3 [7] Barabasi A L 2005 Nature 435 7039 [8] Vazquez A, Oliveira J, Dezso Z 2006 Phys. Rev. E 73 3 [9] Watts D, Strogatz S 1998 Nature 393 6684 [10] Musolesi M, Mascolo C 2007 Mobile Computing and Communications Review 11 3 [11] O’Neill E, Kostakos V, Kindberg T 2006 Ubiquitous Computing 4206 1 [12] Wigner E P 1967 SIAM Review 9 1 [13] Chen Z Q, Zheng R R, Chen H, Yao C Q 2000 Acta Phys. Sin. 49 5 (in Chinese) [陈志谦、 郑仁蓉、 陈 洪、 姚纯青 2000 物理学报 49 5] [14] Chen Z Q, Zheng R R 2001 Chin. Phys. 10 12 [15] Li R, Yan P L, Chen J, Li J, Li J, Zhang K W, Zhong J X 2009 Acta Phys. Sin. 58 10 (in Chinese) [李 蓉、 颜平兰、 陈 健、 李 俊、 李 金、 张凯旺、 钟健新 2009 物理学报 58 10] [16] Zhang F Z, Wang J, Gu Y 1999 Acta Phys. Sin. 48 12 (in Chinese) [张飞舟、 王 娇、 顾 雁 1999 物理学报 48 12] [17] Xing Y Z, Xu G O 1999 Acta Phys. Sin. 48 5 (in Chinese) [邢永忠、 徐躬耦 1999 物理学报 48 5] [18] Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N, Guhr T 2002 Phys. Rev. E 65 6 [19] Yuan J, Mills K 2005 IEEE T DEPEND SECURE 2 4 [20] Sengupta A M, Mitra P P 1999 Phys. Rev. E 60 3

Cited By

•  [1] Bohannon J 2006 Science 314 914 [2] Onnela J O, Saramaki J, Hyvonen J, Szabo G, Lazer D, Kaski K, Kertesz J, Barabasi A L 2007 PNAS 104 18 [3] Marta C G, Cesar A H, Barabasi A L 2008 Nature 453 7196 [4] Hong W, Han X P, Zhou T, Wang B H 2009 Chinese Phys. Lett. 26 2 [5] Ratti C, Williams S, Frenchman D, Pulselli R M 2006 EPB 33 5 [6] Reades J, Calabrese F, Sevtsuk A, Ratti C 2007 IEEE Pervas Comput 6 3 [7] Barabasi A L 2005 Nature 435 7039 [8] Vazquez A, Oliveira J, Dezso Z 2006 Phys. Rev. E 73 3 [9] Watts D, Strogatz S 1998 Nature 393 6684 [10] Musolesi M, Mascolo C 2007 Mobile Computing and Communications Review 11 3 [11] O’Neill E, Kostakos V, Kindberg T 2006 Ubiquitous Computing 4206 1 [12] Wigner E P 1967 SIAM Review 9 1 [13] Chen Z Q, Zheng R R, Chen H, Yao C Q 2000 Acta Phys. Sin. 49 5 (in Chinese) [陈志谦、 郑仁蓉、 陈 洪、 姚纯青 2000 物理学报 49 5] [14] Chen Z Q, Zheng R R 2001 Chin. Phys. 10 12 [15] Li R, Yan P L, Chen J, Li J, Li J, Zhang K W, Zhong J X 2009 Acta Phys. Sin. 58 10 (in Chinese) [李 蓉、 颜平兰、 陈 健、 李 俊、 李 金、 张凯旺、 钟健新 2009 物理学报 58 10] [16] Zhang F Z, Wang J, Gu Y 1999 Acta Phys. Sin. 48 12 (in Chinese) [张飞舟、 王 娇、 顾 雁 1999 物理学报 48 12] [17] Xing Y Z, Xu G O 1999 Acta Phys. Sin. 48 5 (in Chinese) [邢永忠、 徐躬耦 1999 物理学报 48 5] [18] Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N, Guhr T 2002 Phys. Rev. E 65 6 [19] Yuan J, Mills K 2005 IEEE T DEPEND SECURE 2 4 [20] Sengupta A M, Mitra P P 1999 Phys. Rev. E 60 3
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• Received Date:  20 May 2010
• Accepted Date:  13 July 2010
• Published Online:  15 April 2011

Analysis of urban human mobility behavior based on random matrix theory

• 1. Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

Abstract: Mobile communication applications provide a unique data source for the research of human mobility pattern. Based on the distribution data of urban mobile phone users, in this paper is explored the macroscopic dynamical behavior of urban mobility human by using the method of random matrix theory. The largest eigenvalue and the corresponding eigenvector of mobile phone user data deviate far from the distribution of random matrix. The deviations from random matrix vary with time. We find that the largest eigenvalue corresponds to a whole behavior common to all urban human mobility. The results indicate the temporal trends of the mean of correlation coefficient and the largest eigenvalue. We also find that the spatio temporal evolution of the weight of eigenvector components for the eigenvector corresponding to the largest eigenvalue is very consistent with the fluctuation pattern of the macroscopic behavior of urban human mobility.

Reference (20)

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