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uncovering connectivity patterns such as clusters of strongly connected locations
and “hubs,” that is, locations strongly connected to many others. A disadvantage
of the matrix display is the lack of spatial context.
Another way to visualize flows is the flowmap where flows are represented by
straight or curved lines or arrows connecting locations; the flow magnitudes are
represented by proportional widths and/or coloring or shading of the symbols.
Since lines or arrows may connect not only neighboring locations but any two
locations at any distance, massive intersections and occlusions of the symbols
may occur, which makes the map illegible. Several approaches that have been
suggested for reducing the display clutter either involve high information loss
(e.g., due to filtering or low opacity of lesser flows) or work well only for special
cases (e.g., for showing flows from one or two locations).
The other possible way of transforming trajectories to flows is to represent
each trajectory as a sequence of transitions between all visited locations along
the path and aggregate the transitions from all trajectories. Movement data
having sufficiently fine temporal granularity or allowing interpolation between
known positions may be aggregated so that only neighboring locations (adjacent
spatial compartments) are linked by flows. Such flows can be represented on
a flow map without intersections and occlusions of the flow symbols. To sum-
marize movement data in this way, the space can be tessellated into larger or
smaller compartments, for example, using the method suggested in
Andrienko
and Andrienko
(
2011
), to achieve higher or lower degree of generalization and
abstraction. This is illustrated in Figure
8.5
a-c. The same trajectories of cars (a
one-day subset from Wednesday) have been aggregated into flows using fine,
medium, and coarse territory tessellations. The flows are represented by “half-
arrow” symbols, to distinguish movements between the same locations in the
opposite directions. Minor flows have been hidden to improve the display legi-
bility; see the legends below the maps. The exact values of the flow magnitudes
and other flow-related attributes can be accessed through mouse-pointing on the
flow symbols. Flow maps can also be built using predefined locations or space
partitioning, as demonstrated in Figure
8.5
f, where the flow map is built based
on a division of the territory of Milan into 13 geographic regions.
Flow maps can serve as expressive visual summaries of clusters of similar
trajectories. To obtain such summaries, aggregation is applied separately to each
cluster.
When movement data are aggregated into flows by time intervals, the result is
time series of flow magnitudes. These can be visualized by animated flow maps
or by combining flow maps with temporal displays such as a time graph. Flows
may be clustered by similarity of the respective time series (Figure
8.5
d,e) and
the temporal variation analyzed clusterwise, as was suggested for time series
of presence indicators in the previous section. Note that the spatial patterns
visible on the map and the periodic patterns of flow variation visible on the time
