In the last decade, scientists from di erent disciplines discovered a great heterogeneity in human mobility ranges, since a power law characterizes the distribution of the characteristic distance traveled by individuals, the so-called radius of gyration. The origin of such heterogeneity, however, still remains unclear. In this paper, we analyze two mobility datasets and observe that an individual's locations tend to be grouped in dense clusters representing geographical mobility cores. We show that the heterogeneity in human mobility ranges is mainly due to trips between these mobility cores, while it is greatly reduced when individuals are constrained to move within a single mobility core.
In the last decade the availability of big mobility data,
such as GPS tracks from vehicles and mobile phone data,
o ered a series of novel insights on the quantitative patterns
characterizing human mobility. In particular, scientists from
di erent disciplines discovered that human movements are
not completely random but follow speci c statistical laws.
The mobility of an individual can be con ned within a
stable circle de ned by a center of mass and a radius of gyration
[
In this paper, we address this question by performing a data-driven study of human mobility. In our analysis we exploit the access to two mobility datasets, each storing the trajectories of about 50,000 individuals. We observe that the locations visited by the individuals tend to cluster in dense groups, representing meaningful geographical units or mobility cores. We then compute for every individual her inter-core characteristic traveled distance and her intra-core characteristic traveled distance, which are de ned by the radius of gyration computed on the trips between mobility cores and the trips within mobility cores respectively. From the comparison of the total radius of gyration of an individual with her intra- and inter-core radius of gyration we observe two main results. First, a strong linear correlation emerges between the total radius of an individual and her inter-core radius, suggesting that the mobility range of an individual is mainly determined by trips between mobility cores. Second, the distribution of the characteristic intracore radius of gyration has a peak suggesting that individuals show typical mobility ranges when constrained to move within mobility cores. Our results, which emerge on di erent types of mobility data and at di erent geographical and temporal scales, suggest that people perform two types of trips: intra-core trips and inter-core trips, the latter being the origin of the observed heterogeneity in mobility ranges.
The paper is organized as follows. Section 2 summarizes some works relevant to our topic. Section 3 introduces the two mobility datasets we analyze and Section 4 describes the measures of individual human mobility we use during the analysis. Section 5 shows the results of our work and nally Section 6 concludes the paper. 2.
The availability of Big Data on human mobility allowed
scientists from di erent disciplines to discover that
traditional mobility models adapted from the observation of
animals [
The patterns of individual human mobility have been
observed in both GSM data and GPS data [
GSM data. Our rst data source consists of anonymized
mobile phone data collected by a European mobile carrier for
billing and operational purposes. The mobile phones carried
by individuals in their daily routine o er a good proxy to
study the structure and dynamics of human mobility: each
time an individual makes a call the tower that
communicates with her phone is recorded by the carrier, e ectively
tracking her current location. The datasets consists of Call
Detail Records (CDR) describing the calls of 67,000
individuals during three months selected from 1 million users
provided that they visited more than two locations during the
observation period and that their average call frequency was
f 0:5 hour 1. Each call is characterized by timestamp,
caller and callee identi ers, duration of the call and the
geographical coordinates of the tower serving the call. We
reconstruct a user's movements based on the time-ordered
list of phone towers from which a user made her calls [
GPS data. Our second data source is a GPS dataset
storing information about the trips of 46,000 private
vehicles traveling in Tuscany during one month. The GPS traces
are provided by Octo Telematics1, a company that provides
a data collection service for insurance companies. The GPS
device embedded into a vehicle's engine automatically turns
on when the vehicle starts, and the sequence of GPS points
that the device transmits every 30 seconds to the server via
a GPRS connection forms the global trajectory of a vehicle.
We exploit the stops of the vehicles to split the global
trajectory into several sub-trajectories, corresponding to the trips
performed by the vehicle. We set a stop duration threshold
of at least 20 minutes to create the sub-trajectories, in order
to avoid short stops like tra c lights: if the time interval
between two consecutive observations of a vehicle is larger than
20 minutes, the rst observation is considered as the end of a
sub-trajectory and the second one is considered as the start
of another sub-trajectory. We also performed the
extraction of the sub-trajectories by using di erent stop duration
1http://www.octotelematics.com/
thresholds (5, 10, 15, 20, 30 and 40 minutes) without nding
signi cant di erences in the sample of trips and in the
statistical analysis we present in this paper. We assign each origin
and destination point of the obtained sub-trajectories to the
corresponding Italian census cell, using information provided
by the Italian National Institute of Statistics (ISTAT). We
describe the movements of a vehicle by the time-ordered list
of census cells where the vehicle stopped [
GSM vs GPS. The GSM and the GPS datasets di er
in several aspects [
The radius of gyration rg is a standard measure to describe
the characteristic distance traveled by an individual, de ned
as [
N i2L
rcm)2;
(1)
where L is the set of locations visited by the individual,
ri is a two-dimensional vector describing the geographical
coordinates of location i; ni is the visitation frequency of
location i; N = Pi2L ni is the total number of visits of the
individual, and rcm is the center of mass of the individual
de ned as the mean weighted point of the visited locations
[
Given a partition of an individual's locations in m groups, or mobility cores, we de ne a dominant location Di as the most visited location in group i, i.e. the preferred location of the individual when she visits locations in group i (see Figure 1). We de ne the inter-core radius rinter of an individual g as the radius of gyration computed on her m dominant locations (m 2), and the intra-core radius rgintra as the radius of gyration computed on the locations of a given mobility core. Table 1 summarizes the mobility measures we use in our analysis and Figure 1 schematizes some of the concepts introduced above.
measure radius of gyration dominant location intra-core radius of gyration inter-core radius of gyration symbol rg
Di rintra g rinter g
For every individual in the two datasets, we partition her
locations in mobility cores by using the DBSCAN clustering
algorithm [
We compute the distribution of the number of obtained
(non-noise) clusters per individual, at di erent values of eps
parameter (see Figure 2). We observe a peaked distribution
where the majority of individuals have few mobility cores,
e.g. two mobility cores when eps = 5km and one
mobility core when eps = 100km, and individuals having more
than ten mobility cores are extremely rare (Figure 2). The
fact that the algorithm produces non-noise clusters indicates
that that the locations of an individual are not randomly
distributed but tend to aggregated in dense groups of
locations, representing geographical units of individual mobility.
Our distribution of cores per person is in contrast with
previous works which build mobility groups using network
science techniques [
We also compare an individual's radius of gyration rg with her inter-core radius rinter, observing a strong linear correg lation (see Figure 3). Since the inter-core radius is computed on the dominant locations of the individual's mobility cores, this result suggests that the radius of gyration is mainly determined by the tendency of an individual to partition her mobility in di erent geographical units. If we compute the distribution of individuals' intra-core radius rintra, indeed, g 5 # cl1u0sters 15 20
00 2 4 # cl6usters8 10 12 (c) we do not obtain a power law anymore (Figure 4): a peak emerges from the distribution of rgintra for low eps suggesting that, when restricted to move within mobility cores, individuals show typical radii of gyration. In summary, our analysis suggests that: (i) individuals tend to split their mobility in dense groups of locations (mobility cores); (ii) the distance between the dominant locations in mobility cores generates the observed heterogeneity in human mobility ranges; (iii) the heterogeneity is indeed greatly reduced when individuals are constrained to move within mobility cores.
Interestingly, we observe that similar results emerge from both the mobile phone dataset, which captures displacements by any transportation means in an entire European country during three months, and the GPS dataset, which only captures movements by private vehicles occurred in Tuscany during one month.
clusters per user eps = 5km clusters per user eps = 10km 10 40
50 2#0 clusters
30 (a) clusters per user eps = 50km 00 5 10 # c1l5usters20 25 30 clusters per user eps = 100km 14000 12000 10000 s re8000 s u #6000 4000 2000 00
PDF of intra-rg eps = 5km
PDF of intra-rg 0.00 2 4 6intra8-rg [k10m] 12 14 16 0.000 20 40 i6n0tra-rg [k10m0] 120 140 160 80 (a) (b)
In this paper we showed that the locations visited by individuals tend to cluster in a small number of mobility cores. The radius of gyration computed on the dominant locations of each mobility cores highly correlates with the standard radius of gyration, meaning that the characteristic distance traveled by individuals is mainly determined by their dominant locations. Moreover, individuals show homogenous radii of gyration when constrained to travel within mobility cores. Our results showed that individual human mobility is composed by two types of trips: intra-core trips, which represent movement within a given geographical unit, and inter-core trips, which de ne trips between locations belonging to di erent mobility cores and generate the heterogeneity observed in human mobility ranges. As future work, we plan to investigate deeply the structure of intra- and intertrips and quantify the contribution of every single intra- or inter-trip in shaping the characteristic traveled distance of an individual.
This work has been partially funded by the EU under the FP7-ICT Program by project Petra n. 609042, under H2020 Program by projects SoBigData grant n. 654024 and Cimplex grant n. 641191.