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In-Depth Information
(a)15
1,200
150
Φ
max
10
-2
0
0
0
10
-3
-1
-15
-150
-1,200
0
15
-150
0
150
-1,200
0
x
(km)
1,200
10
-4
x
(km)
x
(km)
(b)15
15
15
10
-5
0
0
0
10
-6
Φ
min
-1
-15
-15
-15
0
15
-15
0
x
/
15
-15
0
x
/
15
x
/
σ
x
σ
x
σ
x
Figure 15.5 (a) The probability density function
(
x,y
) of finding a mobile phone user
in a location (
x,y
) in the user's intrinsic reference frame. The three plots, from left to
right, were generated for 10,000 users with:
r
g
≤
3, 20
≤
r
g
≤
30, and
rg >
100 km. The
trajectories become more anisotropic as
r
g
increases. (b) After scaling each position, the
resulting probability distribution has approximately the same shape for each group. Figure
from
Song et al.
(
2009
).
Moreover, the visitation frequency, that is, the probability
f
of a user to visit
a given location, is rather uneven, resulting in a Zipf-like visitation frequency
distribution
P
(
f
)
∼
f
−
(1
+
1
/ζ
)
.
15.1.3 Predictability of Human Mobility
What is the role of randomness in human behavior and to what degree is human
behavior predictable? This question is crucial, because the quantification of the
interplay between the predictable and the unforeseeable is very important in
a range of applications. From predicting the spread of human and electronic
viruses to city planning and resource management in mobile communications,
our ability to foresee the whereabouts and mobility of individuals can help us to
improve or save human lives. In 2009, Song et al. 2009 provided a quantitative
evaluation of the limits in predictability for human walks, using a 3-month-long
mobile phone data set of about 50,000 individuals. The authors defined three
entropy measures: the random entropy
S
rand
i
in the case of location visited with
equal probability; the entropy
S
un
i
that depends only on frequencies of visits;
and the real entropy
S
i
that considers the probability of finding particular time-
ordered subsequences in the trajectory. To characterize the predictability across
the user population, they determined these three entropies per each user
i
,and
