A Multidimensional Model for Correct Aggregation of Geographic Measures - Evolving Application Domains of Data Warehousing and Mining - page 163

of the detailed measure. This basic cube (also
called facts table ) is then enhanced with cells
that contain aggregated values of the measures
for each combination of higher level's members.
Aggregation operators applied on the measures
must be specified in the conceptual model and
depend on the semantics of the application. The
classical functions used to aggregate numeric mea-
sures are the standard SQL operations “COUNT”,
“SUM”, “MIN”, “MAX” and “AVG”. The mul-
tidimensional model allows pre-computation
and fast access to summarized data in support of
multidimensional analysis through OLAP opera-
tors which permit to explore the hypercube. Drill
operators (Roll-Up and Drill-Down) permit to
navigate in the dimensions hierarchies aggregat-
ing measures. Cutting operators (Slice and Dice)
select and project a part of the hypercube. The
multidimensional model and OLAP operators have
been formalized in some logical models (Abello
et al., 2006) as a support to correct aggregation
of measures which plays a central role in multidi-
mensional analysis (Pedersen et al., 2001). They
define constraints on the aggregation functions
in compliance with the semantics of the measure
and explicit the dimensions that can be used in
the multidimensional queries.
Most of 80% of transactional data contain
spatial information, which represents the form
and the location on the earth surface of real world
objects (Franklin, 1992). The heterogeneity of
physical spaces and the strong spatial correlation
of thematic data (Anselin, 1989) are not taken into
account into multidimensional models. Then, a
new kind of systems have been developed, which
intended to integrate the spatial component of the
geographic information into multidimensional
analysis: Spatial OLAP (SOLAP) (Bédard et al.,
2001). Spatial OLAP allows decision-makers to
explore, analyze and understand huge volume of
geo-spatial datasets, in order to discover unknown
and hidden knowledge, patterns and relations.
This useful information can help spatial analysts
and decision-makers to validate and reformulate

decisional hypothesis, and to guide their spatial
decision making processes. SOLAP technologies
have been usefully applied in several domains:
geo-marketing, urban, health, environment,
crisis management, etc. (Bédard et al., 2001)
as they allow non-computer science users to
exploit databases, statistical analysis and spatial
analysis tools without mastering complex query
languages and Geographic Information Systems
functionalities, and understanding underlying
complex spatial datasets. SOLAP redefines main
multidimensional concepts: spatial dimensions,
spatial measures and spatial aggregation func-
tions. In this approach, spatial measures are not
numerical values, but spatial objects (geometries)
which are aggregated using spatial aggregation
functions (union, intersection, etc.) (Shekar et
al., 2001). As shown in this work, SOLAP mod-
els only partially support dependency of spatial
and numerical values, which can lead to wrong
aggregation of spatial and numerical measures
(geographic measures).
In this paper, we identify a three-step ag-
gregation process for the correct aggregation
of geographic measures, and we formalize it by
providing an extension of the logical multidimen-
sional model, GeoCube (Bimonte et al., 2006). The
model provides a set of rules to ensure the valid
aggregation of geographic measures.
This paper is organized as follows. In the Sec-
tion ”Background”, we introduce main concepts
of geographic data and Spatial OLAP. Section
“Related Work” discusses aggregation issues in
multidimensional databases, GIS, geostatistic
and Spatial OLAP domains. We investigate the
problem of the correct aggregation of geographic
measures in the Section “Research Motivations”.
The extension of the multidimensional model Geo-
Cube is presented in Section “Correct Geographic
MultidimensionalAggregation”. Conclusions and
discussions about implementation issues are given
in the Section “Conclusion and Discussion”.