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10 a.m. and to be at home at 10 p.m. Most existing techniques target at near future
movement prediction, such as next minute or next hour. Linear motion functions
[ 30 , 31 , 34 , 35 ] have been extensively studied for movement prediction. More com-
plicated models are studied in [ 36 ]. As pointed out by Jeung et al. [ 17 ], the actual
movement of a moving object may not necessarily comply with some mathemati-
cal models. It could be more complicated than what the mathematical formulas can
represent. Moreover, such models built based on recent movement are not useful for
predicting distant future movement, such as next day or one month after.
Periodic patterns can help better predict future movement, especially for a distant
query time. In [ 17 ], a prediction method based on periodic pattern is proposed. The
prediction problem assumes that the period T and periodic patterns are already given.
To answer predictive queries efficiently, a trajectory pattern tree is proposed to index
the periodic patterns. In [ 17 ], they use a hybrid prediction algorithm that provides
predictions for both near and distant time queries. For non-distant time queries, they
use the forward query processing that treats recent movements of an object as an
important parameter to predict near future locations. A set of qualified candidates
will be retrieved and ranked by their premise similarities to the given query. Then
they select top- k patterns and return the centers of their consequences as answers. For
a distant time queries, since recent movements become less important for prediction,
the backward query processing is used. Its main idea is to assign lower weights to
premise similarity measure and higher weights to consequences that are closer to the
query time in the ranking process of the pattern selection.
4
Pairwise Movement Patterns
In this section, we focus on pattern mining methods on two moving objects. The
pairwise movement patterns are between two moving objects R and S . The trajecto-
ries of two moving objects are denoted as R
=
r 1 r 2 ...r n and S
=
s 1 s 2 ...s m , where
r i and s i are the locations of R and S at the i th timestamp.
We first introduce different similarity measures between two trajectories. Then,
based on properties of patterns, we will introduce generic patterns, behavioral pat-
terns, and semantic patterns. Generic patterns describe the overall attraction and
avoidance relationship between two moving objects. Behavioral patterns describe a
specific type of relationships in a (short) period of time, such as leading and follow-
ing. Semantic patterns tell the semantics of a relationship (e.g., colleague and friend)
in a supervised learning framework.
4.1
Similarity Measure
One way to infer the relationship strength of two moving objects is to measure the
similarity of their trajectories. The simplest way of measuring the similarity between
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