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Figure 6.4 Visual representation of a spatio-temporal sequential pattern.
That means, for instance, that we are interested in what path an individual
follows, but not the hour of the day he/she does it, nor the transportation means
adopted: cars, bicycles, pedestrians, and people on the bus might follow the
same path yet at very different speeds, resulting in different relative times. Also
notice that we are interested here in routes that might be just a small part of a
longer trip of the individual.
The mobility data mining literature provides a few definitions of patterns that
can answer the question given above. In particular, we will briefly summarize
one of the earliest proposals that appeared, at that time generically named spatio-
temporal sequential pattern (in contrast, the trend in recent times is to assign
elaborate and sonorous names to any new form of pattern or model).
The basic idea, also depicted in Figure 6.4 , consists of two steps 4 : first, each
trajectory is cut into quasi-linear segments, and then such trajectory segments
are grouped based on their distance and direction, in such a way that each group
is well described by a single representative segment (see the two thick segments
in the figure); second, consecutive segments are joined to form the pattern.
Frequent sequences are then outputted as sequences of rectangles such that their
width quantifies the average distance between each segment and the points in
the trajectory it covers. Figure 6.4 depicts a simple pattern of this kind, formed
of two segments and corresponding rectangles. In particular, it is possible to
see how the second part of the pattern is tighter than the first one, that is, the
trajectory segments it represents are more compact.
6.3 Global Trajectory Models
A common need in data analysis at large is to understand the laws and rules
that drive the behavior of the investigated objects. In the context of mobility
data mining we refer to such laws and rules as (global) trajectory models,
and in this area we can recognize three important representative classes of
4 The original proposal of this pattern considers a single, long input trajectory. However, the same
concepts can be easily extended to multiple trajectories.
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