A Multidimensional Model for Correct Aggregation of Geographic Measures - Evolving Application Domains of Data Warehousing and Mining - page 178

Figure 9. Correct Geographic Aggregation Mode on Time dimension and using spatial union

Definition. (OverlayGeoObjects)
OverlayGeoObjects is a function which takes
as inputs n Geographic Entity Instances represent-
ing n maps and returns m≥ n Geographic Entity
Instances whose geometries are obtained using
the Union Overlay.
Figure 4 shows the results of the Overlay-
GeoObjects function on geographic objects of
figure 3.
We present now the two Geographic Aggre-
gation Modes for our case study: the first uses
union and the second intersection. We show how
the Geographic Aggregation Mode constraints
oblige the user to use sum only in the first case.
Moreover, these examples show how the user is
forced to aggregate the number of trees consider-
ing the semantics of the attributes and the used
dimensions.
Example 6. Let us consider the query “ Where
and how many trees have been damaged by some
fires during 1978 ?” (Query 1, cf. Sec “Research
Motivations”). We define a View with a Correct
Geographic Aggregation Mode , which uses aver-
age for the Vertical Aggregation and sum and union
for the Horizontal Aggregation (Figure 9).
Formally, let V zones-year = áBC naturalrisks , áS phenomenon ,
S year ñ, Θ zone , γñ represent the Query 1 where:

• Aggregation Mode Θ zone =

áS zone , S zone_agg , Φ union ñ where Φ union is (Figure
5)
1. ϕ geometry : dom(S zone .geometry) n →
dom(S zone_agg .geometry) is Union

Geographic

•

geometry is AF U (spatial aggregation)
2. ϕ nbDamagedtrees : dom(S zone .geometry, S zone .
nbDamagedTrees) n → dom(S zone_agg .nb-
DamagedTrees)= φ nbDamagedTrees where:

ϕ

• φ

nbDamagedTrees is SUM

• κ

nbDamagedTrees = Average

The multidimensional query V zones-year defines
a Correct Geographic Aggregation Mode because
the Geographic Aggregation Mode Constraints
are satisfied:

1. κ nbDamagedTrees ∈ AF ω =Min(DimensionType(n
bDamagedTrees,S year ,S type )

(It is not possible to apply the sum operator
to numbers of trees because this measure is not
additive on time dimension)

2. φ nbDamagedTrees ∈ AF ∑ =SpatialType(AF U ,Min(
SemanticsType(nbDamagedTrees)))

(It is possible to apply the sum to the numbers
of trees for the geographic objects resulting from
VerticalAggregation because the spatial function
is union and it is a spatial aggregation)
The Geographic Aggregation Mode Θ zone uses

• DimensionsMeasure(nbDamagedTrees,

S year , S type ) = AF ω
SemanticsMeasure(nbDamagedTrees) • =

AF ∑