Mobility Data Mining - Mobility Data - page 119

Figure 6.7 Three-dimensional depiction of sample result obtained with time-focused tra-
jectory clustering on a data set of synthetic trajectories.
The simplest solution to the problem is the so-called k-nearest neighbors
(kNN) approach: instead of inferring any classification rule, it directly compares
each new trajectory t against the training set and finds the k labeled trajectories
that are closest to t . The most popular label among the neighbors is then also
assigned to t . The assumption is that the more similar two trajectories are, the
more likely they belong to the same class. Obviously, everything revolves around
a proper choice for the similarity measure applied, which should be as coherent
as possible with the classification problem at hand. As an example, we can
expect that a similarity function that takes into consideration the acceleration of
objects will recognize well the vehicle type - the lighter the vehicle, the easier
it is to reach high accelerations. On the contrary, a measure based only on the
places visited might perform more poorly.
The same idea is also applied in several sampling-based solutions to the
clustering problem: when the data set is too large to process, one approach
consists of randomly sampling a small subset of trajectories and computing
clusters on them. Then, all other trajectories are assigned to the cluster (i.e.,
classified) with a kNN approach or by comparing them against the centroid of
each cluster.
Approaching the problem from a different viewpoint, each class involved in
the classification problem could be modeled through a probabilistic model that
is fitted to the available trajectories in the class. Then, each new trajectory can be