Trajectory Data Warehouses - Mobility Data - page 78

sumDuration : sum of the durations of the trajectories.
velocity : average speed of the trajectories.
acceleration : average change of speed of the trajectories.
crossX , crossY , crossT : total number of distinct trajectories crossing the
border between the cell and its adjacent cells, along the spatial ( X and Y )and
temporal ( T ) axes. These measures will be explained in Section 4.6.1 .
We remark that these measures represent aggregated numeric information
about trajectories. Thus, no spatio-temporal information about trajectories is
recorded in the TDW whatsoever. This information lies only in the moving
object database, and can be used for answering queries, along with the data
in the TDW, when detailed (nonaggregated) information is required. Formally
speaking, according to the definitions given in Section 4.4 , the data warehouse
in Figure 4.5 is a spatial data warehouse. Although useful in many practical situ-
ations, this approach does not suffice for a comprehensive analysis of movement
data (see Section 4.8 ).
4.6.1 The Double-Counting Problem
As we have seen, the individual trajectories are not stored in the GeoPKDD
TDW; only aggregate information is kept. As result, the double-counting prob-
lem may appear during aggregation over the partitioned space. We use the
measure presence , explained above, to show the problem. Consider the three
trajectories over the space divided into six regions R1 through R6 in Figure 4.6 .
If we perform a roll-up to aggregate the number of trajectories in regions R4,
R5, and R6 (suppose they constitute a district), we would obtain a total of six
trajectories (resulting from adding three trajectories in R4, two in R5, and one
in R6), while the correct number to obtain would have been three trajectories.
Solving this problem requires accessing the moving object database to com-
pute super-aggregates in all dimension levels. This problem may occur while
answering the following query.
Query 4.8. “Give the number of trajectories per district on January 1, 2010.”
In the above query, the measure presence must be aggregated over all the
cells that belong to a district. A first solution would be to simply sum up the
measure values of these cells. In the literature, this is a common, although very
imprecise, approach to aggregating spatio-temporal data.
Another approach uses linear interpolation to prevent omitting in the result
the cells crossed by a trajectory but in such a way that no sample point of the
trajectory occurred within them. This approach borrows from statistical methods
to deal with the double-counting problem. The basic idea is the following.
Let us denote pres C x,y,t the presence measure in a given cell C x,y,t .Given