Multi-scale spatio-temporal analysis of human mobility

RESEARCH ARTICLE Multi-scale spatio-temporal analysis of human mobility Laura Alessandretti1, Piotr Sapiezynski2, Sune Lehmann2,3, Andrea Baronchelli1* 1 City, University of London, London EC1V 0HB, United Kingdom, 2 Technical University of Denmark, DK2800 Kgs. Lyngby, Denmark, 3 Niels Bohr Institute, University of Copenhagen, DK-2100 København Ø, Denmark * a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Alessandretti L, Sapiezynski P, Lehmann S, Baronchelli A (2017) Multi-scale spatio-temporal analysis of human mobility. PLoS ONE 12(2): e0171686. doi:10.1371/journal.pone.0171686 Editor: Tobias Preis, University of Warwick, UNITED KINGDOM Abstract The recent availability of digital traces generated by phone calls and online logins has significantly increased the scientific understanding of human mobility. Until now, however, limited data resolution and coverage have hindered a coherent description of human displacements across different spatial and temporal scales. Here, we characterise mobility behaviour across several orders of magnitude by analysing *850 individuals’ digital traces sampled every *16 seconds for 25 months with *10 meters spatial resolution. We show that the distributions of distances and waiting times between consecutive locations are best described by log-normal and gamma distributions, respectively, and that natural time-scales emerge from the regularity of human mobility. We point out that log-normal distributions also characterise the patterns of discovery of new places, implying that they are not a simple consequence of the routine of modern life. Received: November 14, 2016 Accepted: January 24, 2017 Published: February 15, 2017 Copyright: © 2017 Alessandretti et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: Data used to generate Fig.3, Fig.5, Fig.6 and Fig.7 can be found at https://figshare.com/s/f424d0c0d1721365950d (DOI: 10.6084/m9.figshare.4596346). Data used to generate Fig.4 can not be shared due to privacy consideration regarding subjects in our dataset, including European Union regulations and Danish Data Protection Agency rules. The data contains detailed information on mobility and daily habits of 850 individuals at a high spatio-temporal resolution. We understand and appreciate the need for transparency in research and are ready to make the data available to researchers who meet the criteria for access to confidential data, sign a Introduction Characterising the statistical properties of individual trajectories is necessary to understand the underlying dynamics of human mobility and design reliable predictive models. A trajectory consists of displacements between locations and pauses at locations, where the individual stops and spends time (Fig 1). Thus, the distribution of waiting times (or pause durations), Δt, between movements and the distribution of distances, Δr, travelled between pauses are often used to quantitatively assess the dynamics of human mobility. For example, specific probability distributions of distances and waiting times characterise different types of diffusion processes. Thanks to the recent availability of data used as proxy for human trajectories including mobile phone call records (CDR), location based social networks (LBSN) data, and GPS trajectories of vehicles, the characteristic distributions of distances and waiting times between consecutive locations have been widely investigated. There is no agreement, however, on which distribution best describes these empirical datasets. Pioneer studies, based on CDR [1, 2] and banknote records [3], found that the distribution of displacement Δr is well approximated by a power-law, P(Δr) * Δr−β, (or ‘Lévy distribution’ [4], as typically 1 < β < 3), and that an exponential cut-off in the distribution may control boundary effects [2]. These findings were confirmed by studies based on GPS trajectories of PLOS ONE | DOI:10.1371/journal.pone.0171686 February 15, 2017 1 / 17 Multi-scale spatio-temporal analysis of human mobility confidentiality agreement, and agree to work under our supervision in Copenhagen. Please direct your queries to Sune Lehmann, the Principal Investigator of the Copenhagen Network Study, at . Funding: This work was supported by Villum Foundation, http://villumfoundation.dk/ C12576AB0041F11B/0/ 4F7615B6F43A8EA5C1257AEF003D9930? OpenDocument, Young Investigator programme 2012, High Resolution Networks (SL) and University of Copenhagen, http://dsin.ku.dk/news/ ucph_funds/, through the UCPH2016 Social Fabric grant (SL). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. individuals [5–7] and vehicles [8, 9], as well as online social networks data [10–12]. It has been noted, however, that power-law behaviour may fail to describe intra-urban displacements [13]. Other analyses, based on online social network data [14–16] and GPS trajectories [17–20] showed that the distribution of displacements is well fitted by an exponential curve, P(Δr) * e−λΔr, in particular at short distances. Finally, analyses based on GPS on Taxis [21, 22] suggested that displacements may also obey log-normal distributions, 2 P(Δr) * (1/Δr)  e−(log Δr − μ) /2σ2. In Ref. [6], the authors found that this is the case also for single-transportation trips. Fewer studies have explored the distribution of waiting times between displacements, Δt, as trajectory sampling is often uneven (e.g., in CDR data location is recorded only when the phone user makes a call or texts, and LBSN data include the positions of individuals who actively “check-in” at specific places). Analyses based on evenly sampled trajectories from mobile phone call records [1, 23], and individuals GPS trajectories [5, 7] found that the distribution of waiting times can be also approximated by a power-law. A recent study based on GPS trajectories of vehicles, however, suggests that for waiting times larger than 4 hours, this distribution is best approximated by a log-normal function [24]. Several studies have highlighted the presence of natural temporal scales in individual routines: distributions of waiting times display peaks in that corresponds to the typical times spent home on a typical day (*14 hours) and at work (*3 − 4 hours for a part-time job and *8 − 9 hours for a fulltime job) [23, 25, 26]. Fig 2 and Table 1 compare distributions obtained using different data sources. The spectrum of results reflects the heterogeneity of the considered datasets (see Fig 2). It is known in fact that data spatio-temporal resolution and coverage has an important influence on the results of the analyses perfor (...truncated)