Mobility Data Mining - Mobility Data - page 117

(a) (b)
Figure 6.6 Sample trajectory clustering on a real data set of vehicles (GPS data collected
by OctoTelematics S.p.A.), obtained using a density-based clustering schema and a spatial
route distance function. (See color plate.)
Spatial route: In this case, the spatial shape of the trajectory is considered,
and two trajectories that follow a similar path (though possibly at different
times and with different speeds) from start to end will result in a low distance.
Spatio-temporal route: In this case, the time is also considered, therefore two
trajectories will be similar when they approximately move together through-
out their life.
Obviously, the selection of the clustering schema and the selection of the
distance function might also be performed in the opposite order. Indeed, in some
cases the choice of the distance to adopt is relatively easy or even enforced by
the specific application, in which case the selection of the distance is performed
first.
Figure 6.6 b shows an example of a result obtained by a specific combination
of schema and distance, namely a density-based clustering algorithm using
the spatial route distance described above. Different clusters are plotted with
different colors. The data set used in the example contains trajectories of vehicles
in Tuscany, Italy, also plotted on Figure 6.6 a.
Trajectory-oriented clustering methods. A complementary approach to clus-
tering, as opposed to the distance-based solutions described so far, consists in
algorithms that try to better exploit the nature and inner structure of trajectory
data. From a technical point of view, that usually translates to deeply readapting
some existing solution in order to accommodate the characteristics of trajectory
data.
One important family of solutions makes use of standard probabilistic model-
ing tools. Avery early examplewas provided by mixturemodels-based clustering
of trajectories. The basic idea is not dissimilar from k -means: we assume that
the data actually form a set of k groups, and each group can be summarized by