Geoscience Reference
In-Depth Information
15.4
Exploring Temporal Patterns
15.4.1
Typical Week Signature
To minimize the impact of special events on the datasets, we followed the procedure
presented in Reades et al. (
2007
) to extract average “typical week” timelines for each
pixel at each 15-min interval, using the three-month period. The values of the typical
weeks for a given 15-min time interval were calculated as the average of the same
intervals from the whole measurement. For example, the typical number of calls for
12:00 to 12:15 on the typical Monday was taken as the average number of calls from
12:00 to 12:15 on every Mondays available in the dataset. Civic holidays, considered
as special events, were excluded from the computation to avoid the introduction of
unnecessary noise. We use these mathematical notations:
A
i
.t /, to measure activity of type (number of calls, SMS or request, volume
of data upload or download) within a given pixel i at time t
2
Œ1; 672 (since the
measurements are taken every 15-min, one week comprises 7
96
D
672 time
intervals)
A
city
.t /, to measure activity of type (number of calls, SMS or request, volume
of Data upload or download) within a given city at time t
2
Œ1; 672
In order to better compare the relative dynamic patterns across the cities'
locations (e.g., recognizing locations with similar patterns up to multiplicative
constant due to higher active population density), it is useful to normalize these
values by the typical amplitude of activities on each pixel. We thus define the
signature S
i
of activity type on location i thanks to a mean normalization:
S
i
.t /
D
A
i
.t /=
h
A
i
i
t
;
(15.1)
where
h
:::
i
t
denotes an average over the 672 individual 15-min time intervals of a
typical week. Similarly, the signature S
city
of activity type at the city scale is given
by
S
city
.t /
D
A
city
.t /=
h
A
city
i
t
:
(15.2)
As an illustration of the computation of signatures, Fig.
15.3
a displays the
mean-normalized call timeline in Greater London over the three-month observation
period. This timeline shows daily variations - with peaks of activity during the
days and drops of activity at nights - and weekly variations, with daily peaks
significantly lower during weekends than during workdays. Figure
15.3
b then shows
how this timeline can be decomposed into a repeating typical week pattern and a
residual part. The residual part accounts for special events, such as the occurrence
of civic holidays (notice the lower amount of calls on April 1, May 6, and May 27,
respectively, Easter, May Bank, and Spring Bank holidays in London), and general
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