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a computational procedure that finds for each trajectory position the closest
position in another trajectory within a given time window, for example, of 1
minute length (from
−
30 to
+
30 seconds with respect to the time of the current
position).
The location types could be taken from an additional data set describing the
streets; however, we have no such data set for Milan. We shall demonstrate the
use of previously derived data. Earlier we made a tessellation of the territory
(Figure
8.4
); moreover, the clustering according to the temporal variation of the
car presence (Figure
8.4
d) separates quite well the cells on motorways from the
other cells. We create a suitable classification of the cells, as in Figure
8.6
d,
by editing the clusters. Here the yellow filling corresponds to the cells on
motorways. We select this class of cells and compute the distances from the
trajectory positions to the selected cells; for each position the nearest cell is taken.
The computed distances are attached to the position records as a new attribute,
which can now be used for filtering. By filtering, we extract the points and
segments of the trajectories with zero distances to the selected cells (Figure
8.6
d).
We compute also the distance from each position to the nearest position of
another car within the 1-minute time window. This makes one more attribute
attached to the position records. Then we use an additional filter according
to values of this attribute to sequentially select the trajectory points with the
distances to the nearest neighbor in three different ranges: below 20 m, from
20 to 50 m, and over 50 m. For each subset of points, we produce a frequency
histogram of the respective speeds. The histograms are shown in Figure
8.6
a-c.
They have the same height and bar width. The latter corresponds to a speed range
of approximately 5 km/h. Hence, despite the differing sizes of the point subsets,
the shapes of the distributions can be compared. There are many points with
low speeds (0-10 km/h) in each subset but the relative number of such points is
the highest in the first subset and the lowest in the third subset. In all subsets,
there is a smaller peak of frequencies for the speeds 80-90 km/h, but this peak
is the lowest for the first subset and the highest for the third subset. Hence, we
observe that smaller distances between cars on a motorway correspond to lower
movement speeds.
To demonstrate investigation of occurrent relationships between moving
objects and items of the context, we extract from the car trajectories the events
where the car is on a motorway and its distance to the nearest neighbor car
is at most 10 m while the movement speed is not more than 10 km/h. These
events reflect occurrent proximity relationships of cars to motorways and other
cars while the low speeds indicate that these occurrences may be related to
traffic congestions. As we did in Section
8.3
, we find spatio-temporal clusters
of these events; some of them are shown in the STC in Figure
8.6
e. We build
spatio-temporal convex hulls around the event clusters (the yellow shapes in
Figure
8.6
e). We assume that each convex hull represents a traffic jam. Hence,
