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teristic travel distance and a significant probability to return to a few
highly frequented locations. On further simplification, it was shown that
individual travel patterns collapse into a single spatial probability distri-
bution. This suggests that humans follow simple reproducible patterns.
This simple observation has consequences for all phenomena driven by
human mobility, such as epidemic prevention, emergency response, ur-
ban planning and agent-based modeling.
A key area of research for mobile trajectory analysis is to determine
frequent and repetitive trajectories in the data. The most basic analy-
sis from this perspective is to determine similar trajectories to a given
target trajectory. A variety of methods on the topic of indexing mov-
ing object databases may be found in [80]. The problem has also been
studied in the context of the gps trajectories created by mobile phones
[43, 174]. A method for performing user-oriented trajectory search for
trip recommendations has been proposed in [147].
More generally, the work in [70] explores the sequential pattern min-
ing problem in the context of trajectory pattern mining. The idea is
to determine sequences of places in the data, which occur together fre-
quently in the data, and with similar transition times. The sequential
pattern mining paradigm can be extended to this case by incorporating
temporal constraints into successive elements of the sequence.
Trajectory patterns can also be derived from geo-tagged photos, in
which users utilize gps-enabled mobile phones to take photos and up-
load them. Since the user location and time is recorded, when they take
the photo, this provides natural way to derive the trajectory of the user.
For example, the work in [171] mines frequent sequential trajectory pat-
terns from such geo-tagged social media. However, the number of pat-
terns may be too large to be informative to a user. Therefore, a ranking
mechanism is introduced in order to determine the importance of the
different reported patterns. The relationships between users, locations
and patterns and their importance are utilized for ranking purposes. For
example, trajectories are considered important, if they are followed by
important users, and contain important locations. The vice-versa re-
lationships also hold in this case. These importance relationships are
modeled in [171] with the use of matrices representing the pairwise rela-
tionships between users, locations and patterns. A system of equations
is set up with these matrices and solved in order to determine the impor-
tance values of the different trajectories. In addition, a
diversification
criterion
is introduced in order to ensure that trajectories with large seg-
ments in common are not reported simultaneously. This is done in order
to maximize the amount of useful in information in a small number of
presented results. The GPS data can also be used in order to determine
