On Modeling and Analysis of Multidimensional Geographic Databases - Data Warehousing Design and Advanced Engineering Applications - page 101

Figure 2. Multidimensional model with spatial dimension

Descriptive attributes of geographic data could
be useful to the spatio-multidimensional decisional
process. Thus, Bimonte (2008) introduces the
concept of “Geographic Measure”.A “Geographic
Measure” is a geographic object described by
alphanumeric and spatial attributes. Moreover, it
could belong to one or many hierarchy schemas.
This establishes a complete symmetry of geo-
graphic measures and geographic dimensions.
Replacing the spatial measure of the multidi-
mensional application in the previous example
with the geographic measure representing cities
(see Figure 3b), it should be possible to answer
queries like: “What cities, their population, and
their socio-economic types, are polluted by CO2
per month?” Indeed, a city is a geographic object
described by geometry and two alphanumeric
attributes: population and socio-economic type.
Note that a (spatial) aggregation function is ap-
plied to each (spatial) attribute of the geographic
measure (i.e. topological union for geometry,
list for name, sum for population and a ratio for
socio-economic type).
Spatio-multidimensional operators extend
drill and cut OLAP operators. “Spatial Roll-up”
and “Spatial Drill-down” authorize to navigate
into spatial dimensions by the simple interaction
with the map component of the SOLAP user-
interface (Rivest et al., 2005). “Spatial Slice”

makes possible cutting the spatial hypercube by
selecting directly spatial members through SO-
LAP user-interface (Rivest et al., 2005), using
spatial/alphanumeric predicates (Sampaio et al.,
2006) or spatial analysis operators such as buffer
(Scotch & Parmanto, 2006). Exploiting the sym-
metrical representation of geographic dimensions
and measures, Bimonte (2008) proposes two
operators, “Permute” and “Measure navigation”.
“Permute” allows exchanging dimension and
geographic measure. This operator dynamically
modifies the structure of the spatial hypercube.
“Measure navigation” allows navigating into
the geographic measure's hierarchy, changing
granularity of the measure on the fly. For instance,
since cities belong to departments (Figure 3b),
“Measure navigation” operator permits to analyze
polluted French departments (instead of cities)
along time and pollutants dimensions. Moreover,
to make the spatio-multidimensional paradigm
more flexible and being closer to spatial analysis
process, Bimonte et al. (2007b) propose a new
kind of operators which change the structure of
the spatial hypercube through the introduction of
new spatial members into geographic dimension
thanks to spatial analysis operators.