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map's scale, reduce visualized features, access
to alphanumeric information using the map,
etc. Sometimes, maps provide also an interface
to advanced (visual) analysis techniques. Users
can explore alphanumeric data, perform complex
analysis methods, and obtain personalized and
complex visual representations of data by simply
interacting with map's features (interactive maps).
Interactive maps are the basis of geovisualization
systems (MacEachren, et al., 2004). Such systems
integrate scientific visualization and image analy-
sis techniques, and GIS tools into an interactive,
flexible and user-friendly framework in order to
explore and analyze spatial data. Interactive capa-
bilities are mandatory for spatial decision-making
process (MacEachren & Kraak, 1997).
level. Map generalization is the process used to
derive data and maps for secondary scales and/or
themes, preserving a good and clear representation
focused on the goal of the map (Weibel & Dutton,
2001). Map generalization provides a simpli-
fied vision of the spatial phenomenon enriching
spatio-multidimensional analysis capabilities and
improving SOLAP clients' visualization.
An example of SOLAP application using a spa-
tial dimension is a study for pollution supervision
in French cities. This multidimensional application
presents three dimensions: “Time”, “Pollutants”,
and “Location” (spatial dimension), and a nu-
merical fact, “Pollution”. This fact is depicted by
three measures giving minimum, maximum and
average pollution values (see Figure 2) (Bimonte
et al., 2007a). This multidimensional application
answers questions like “What are the average,
min and max values per month, and pollutant for
departments with population above 2M?”
A very different way to introduce spatial infor-
mation in data warehouses is using it as an analysis
subject, i.e. as a fact. Different definitions of the
spatial measure can be found in literature: a collec-
tion of geometries (spatial objects) (Stefanovic et
al., 2000; Rivest et al. 2001), geometries or numeri-
cal values resulting from spatial (i.e. topological
and metric) operators (Malinowsky & Zimányi,
2004), and/or spatial members (Marchand et al.,
2003). Spatial aggregations (i.e. union, intersec-
tion, etc.) replace SQL SUM, MIN, MAX, AVG,
and COUNT functions. Maps, then, are the cells
of the hypercube.
Let us take the spatio-multidimensional model
given in figure 3a. The spatial attribute of the
“City” level of application of figure 2 is now used
as spatial measure. The spatial measure is aggre-
gated using the topological union. Pollution values
grouped by 5mg/l are used as analysis dimension.
This model analyzes polluted French cities ac-
cording to time, pollutants and pollution values.
In this model, the user should be able to deduce
information about the influence of geographical
location of cities in the pollution problem.
SPATIO-MULTIDIMENSIONAL
DATABASES: MODELS AND TOOLS
Spatio-Multidimensional Models
The more natural and common manner to integrate
spatial information into multidimensional models,
is to use it as a dimension. As defined in Bédard et
al. (2001), a spatial dimension can be “spatial non
geometric” (i.e. with text only members), “spatial
geometric” (i.e. with members with a cartographic
representation) or “mixed spatial” (i.e. combining
cartographic and textual members). Malinowsky
& Zimányi (2005) define a spatial dimension as a
set of spatial hierarchies. A “spatial hierarchy” is
a hierarchy with at least one level with the spatial
attribute (spatial level). Topological intersection or
inclusion relationships exist between members of
different spatial levels. Bimonte (2008) proposes
the concept of “Geographic Dimension” enrich-
ing spatial dimensions with “Map Generalization
Hierarchies”. “Map Generalization Hierarchy”
represents geographic information at different
scales or according secondary themes where the
members of a level are the result of map generaliza-
tion operators applied to the members of the lower
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