Database Reference
In-Depth Information
(a) (b)
Figure 7.2 Cumulative frequency distribution of trajectories in space. (a) The plot proposes
a ranked list of three candidate values for the T-pattern support threshold (13, 24, 82) based
on detected points of significant slope variation. (b) Cumulative distribution of transition
times between each pair of points in each trajectory.
of significant slope change in this distribution are the best candidates for the
support threshold, because these points separate groups of grid cells that have a
rather uniform frequency internally, while the frequency between the different
groups is very different.
Another crucial parameter for the extraction of T-pattern is the time tolerance
τ
. In Figure
7.2
a we plot all the time distances for every possible pair of points in
each trajectory. These represent all the possible transition time candidates in the
T-patternmining algorithm. The sharp steps in the zoomed inset are the artifact of
the average sampling rate,
≈
33 seconds. This is the minimum admissible value
for the
τ
parameter. We note that with a high value of
τ
the T-pattern computation
aggressively merges the transition times. For instance, with 130 seconds 10% of
transition times are merged. An adequate candidate for the
τ
parameter is around
the 50th percentile (14 minutes) and, in any case, between the 10th and the 90th
percentiles (2 minutes-45 minutes). The frequency distribution of trajectories
in M-Atlas is realized computing the
intersection
between the spatial grid and
the set of trajectories as specified in the following query:
CREATE RELATION intersection_table USING INTERSECT
FROM (SELECT t.id, t.object, s.id, s.object
FROM <trajectories_table> t, <grid_cells> s)
and grouping the result by the cells. We see the use of the
RELATION
query with
the
INTERSECT
operation that here applies to trajectories and spatial objects.
Once the presence of trajectories in the spatial cells is computed by this query, a
frequency distribution has to be computed. Therefore, the cumulative distribution
and the identification of the slopes can be done using the mathematical functions
provided by standard SQL.
