Database Reference
In-Depth Information
Visualization by animated density/presence maps and change maps is possible
as in the case of continuous surfaces. There are also other possibilities. The time
series may be shown in an STC by proportionally sized or shaded or colored
symbols, which are vertically aligned above the locations; Figure
8.4
cgives
an example; the color legend is given in the lower right corner of Figure
8.4
.
Occlusion of symbols is often a serious problem in such a display; therefore, we
have applied interactive filtering so that only the data for the most intensively
visited cells (1,000 or more visits per day) are visible.
When the number of the space compartments is big and the time series is
long, it may be difficult to explore the spatio-temporal distribution of object
presence using only visual and interactive techniques. It is reasonable to cluster
the compartments by similarity of the respective time series and analyze the tem-
poral variation cluster-wise, that is, investigate the attribute dynamics within the
clusters and do comparisons between clusters. Figure
8.4
d demonstrates the
outcome of
k
-means clustering of grid cells according to the time series of
car presence obtained by aggregating the car movement data from the whole
time period of one week by hourly intervals (hence, the time series consists
of 168 time steps). Distinct colors have been assigned to the clusters and used
for painting the cells on the map. The same colors are used for drawing the
time series lines on the time graph in Figure
8.4
e. The colours are chosen by
projecting the cluster centroids onto a 2D continuous color map; hence, clusters
with close centroids receive similar colors and, vice versa, high difference in
colors signifies much dissimilarity between the clusters. Figure
8.4
e shows a
prominent periodic variation of car presence in the grid cells over the week.
Interactive tools allow us to select the clusters one by one or pairs of clusters
for comparison and see only these clusters on the displays. We find out that the
clusters differ mainly in the value magnitudes and not in the temporal patterns
of value variation, with the exception of the bright red and orange clusters. The
value ranges in these clusters are very close. The main difference is that the red
cluster has higher values in the afternoons of Sunday and Saturday. This may
have something to do with people spending their leisure time near lakes, which
are located to the north of the city.
Spatially referenced time series is one of two possible views on a result of
discrete spatio-temporal aggregation. The other possibility is to consider the
aggregates as a temporal sequence of
spatial situations
. The term “spatial situ-
ation” denotes spatial distribution of aggregate values of one or more attributes
in one time interval. Thus, in our example, there are 168 spatial situations, each
corresponding to one of the hourly intervals within the week. Temporal variation
of spatial situations can also be investigated by means of clustering. In this case,
the spatial situations are considered as feature vectors characterizing different
time intervals. Clustering groups the time intervals by similarity of these feature
vectors.
