Database Reference
In-Depth Information
8.4.1 Analyzing Presence and Density
Presence of moving objects in a location during some time interval can be
characterized in terms of the count of different objects that visited the location,
the count of the visits (some objects might visit the location more than once),
and the total time spent in the location. Besides, statistics of various attributes
describing the objects, their movements, or their activities in the location may
be of interest. To obtain these measures, movement data are aggregated spatially
into continuous density surfaces or discrete grids. Density fields are visualized
on a map using color coding and/or shading by means of an illumination model
(Figure
8.4
a). Density fields can be built using kernels with different radii and
combined in one map to expose simultaneously large-scale patterns and fine
features, as demonstrated in Figure
8.4
a.
An example of spatial aggregation using a discrete grid is given in Figure
8.4
b.
The irregular grid has been built according to the spatial distribution of points
from the car trajectories. The darkness of the shading of the grid cells is propor-
tional to the total number of visits. Additionally, each cell contains a circle with
the area proportional to the median duration of a visit. It can be observed that
the median duration of staying in the cells with dense traffic (dark shading) is
mostly low. Longer times are spent in the cells in the city center and especially
at the Linate airport in the east. There are also places around the city where the
traffic intensity is low while the visit durations are high.
To investigate the temporal variation of object presence and related attributes
across the space, spatial aggregation is combined with temporal aggregation,
which can also be continuous or discrete. The idea of spatial density can be
extended to spatio-temporal density: movement data can be aggregated into
density volumes in a 3D space-time continuum, which can be represented in an
STC.
For discrete temporal aggregation, time is divided into intervals. Depending
on the application and analysis goals, the analyst may consider time as a line
(i.e., linearly ordered set of moments) or as a cycle, for example, daily, weekly, or
yearly. Accordingly, the time intervals for the aggregation are defined on the line
or within the chosen cycle. The combination of discrete temporal aggregation
with continuous spatial aggregation gives a sequence of density surfaces, one
per time interval, which can be visualized by animated density maps. It is also
possible to compute differences between two surfaces and visualize them on a
map, to see changes occurring over time (this technique is known as a change
map).
The combination of discrete temporal aggregation with discrete spatial aggre-
gation produces one or more aggregate attribute values for each combination of
space compartment (e.g., grid cell) and time interval. In other words, each space
compartment receives one or more time series of aggregate attribute values.
