A Density-Based Clustering of Spatio-Temporal Data - New Contributions in Information Systems and Technologies - page 38

Fig. 1. An example of trajectory clustering in the partition-and-group framework [7]

Generalized Spatio-Temporal Locality In-between Polylines (GenSTLIP) is a
method introduced to measure the similarity between trajectories [8]. It is a time-
aware function that gives an indication of how similar two trajectories are to each
other. This function considers the spatial parameters by calculating the area between
the two trajectories (LIP) and considers the temporal parameter by calculating the
local temporal distance (TLIP) between them.

, = ∑

.

,,,

(1)

Where: & are two whole trajectories being compared
: User's assigned importance to the time-factor
: Tolerance in the past and future between two trajectories

= · 1· .

(2)

Where: calculates the area of the shape formed by the two 2D polylines that
correspond to the routes of the two trajectories.
: is a measure in the range [0, 1] modeling the temporal distance

.

= 12·

(3)

Where: Maximum duration intersection between two segments
1 2 : The time duration of each sub-trajectory
Figure 2 represents an example showing two trajectories (S & Q) being compared
using the GenSTLIP function. As seen in the above equation, GenSTLIP is the
summation calculated for sub-trajectories. LIP and TLIP are calculated for each two
sub-trajectories being compared and added up to give an indication of the similarities
between the trajectories as a whole.