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understanding of the data. New analytical questions arise as an outcome of the
previous analysis and determine the further steps. The whole process is called
“progressive clustering” (
Rinzivillo et al.
,
2008
).
There is an implementation of the density-based clustering algorithmOPTICS
in which the process of building clusters is separated from measuring the dis-
tances between the objects. This allows clusteringwith the use of diverse distance
functions. Hence, the procedure of progressive clustering is done as follows: The
user chooses a suitable distance function and applies the clustering tool first to
the whole set of trajectories. Then the user interactively selects one or more clus-
ters and applies the clustering algorithm to this subset using a different distance
function or different parameter settings. The last step is iterated. In this way,
the user may (1) refine clustering results, (2) combine several distance functions
differing in semantics, and (3) gradually build comprehensive understanding of
different aspects of the trajectories.
The procedure of progressive clustering is illustrated in Figure
8.2
. The first
image, Figure
8.2
a, shows the result of clustering of the same subset of the car
trajectories as in Figure
8.1
using the distance function “common destinations,”
which compares the spatial positions of the ends of trajectories. From the 8,206
trajectories, 4,385 have been grouped into 80 density-based clusters and 3,821
treated as noise. Figure
8.2
b shows the clusters without the noise. We have
selected the biggest cluster, consisting of 590 trajectories that end in the north-
west (Figure
8.2
c), and applied clustering with the distance function “route sim-
ilarity” to it. This distance function compares the routes followed by the moving
objects. Figure
8.2
d presents the 18 clusters we have obtained; the noise
consisting of 171 trajectories is hidden. The largest cluster (in red) consists of
116 trajectories going from the city center and the next largest cluster (in orange)
consists of 104 trajectories going from the northeast along the northern motor-
way. The orange cluster and the yellow cluster (68 trajectories) going from the
southeast along the motorways to the south and west are, evidently, trajectories
of transit cars. The clusters by route similarity are also shown in the STC in
Figure
8.2
e. This display involves time transformation, which is discussed in the
next subsection.
8.2.3 Transforming Times in Trajectories
Comparison of dynamic properties of trajectories using STC, time graph, or
other temporal displays is difficult when the trajectories are distant in time,
because their representations are located far from each other in a display. This
problem can be solved or alleviated by transforming times in trajectories. Two
classes of time transformations are possible:
1. Transformations based on temporal cycles: Depending on the data and appli-
cation, trajectories can be projected in time onto a single year, season, month,
