A Multidimensional Model for Correct Aggregation of Geographic Measures - Evolving Application Domains of Data Warehousing and Mining - page 179

Figure 10. Correct geographic aggregation mode on time dimension and using spatial intersection

spatial Union (ϕ geometry ) to aggregate geometry. The
aggregation of the number of damaged trees is per-
formed using theAVG for the vertical aggregation
(κ nbDamagedTrees ), as the number of damaged trees is
not additive on time dimension (DimensionsMea
sure(nbDamagedTrees, S year , S type ) = AF ω ), and the
SUM (φ nbDamagedTrees ) for the horizontal aggregation,
as ϕ geometry is a spatial aggregation (AF U ).
Example 7. Let us suppose now we want to
answer to the query “ Where and how many trees
have been damaged by all fires during 1978? ”
(Query 2, cf. Sec “Research Motivations”). We
define a View with a Correct Geographic Aggrega-
tion Mod e, which uses an interpolation function
and intersection for the Horizontal Aggregation ,
and average for the Vertical Aggregation (Figure
10).
Let Θ zone = áS zone , S zone_agg , Φ intersect ñ (Query 2)
where Φ intersect is:

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

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

(The sum cannot be applied to numbers of
trees because this measure is not additive on time
dimension)

2. φ nbDamagedTrees ∈ AF ω = SpatialType(AF Ω , Mi
n(SemanticType(nbDamagedTrees)))

(The sum cannot be applied to numbers of
trees of the geographic objects resulting from
VerticalAggregation because the spatial function is
intersection and it is a spatial disaggregation).
The Geographic Aggregation Mode Θ zone uses
spatial Intersection (ϕ geometry ) to aggregate geom-
etry. The aggregation of the number of damaged
trees is performed using the AVG for the vertical
aggregation (κ nbDamagedTrees ), as the number of dam-
aged trees are not additive on time dimension (D
imensionsMeasure(nbDamagedTrees, S year , S type )
= AF ω ), and the Weighted Average on surface
(φ nbDamagedTrees ) for the horizontal aggregation, as
ϕ geometry is a spatial disaggregation (AF Ω ).
We have presented and illustrated the approach
we propose for Correct Geographic Aggregation

1. ϕ geometry : dom(S zone .geometry) n →
dom(S zone_agg .geometry) is Intersection
ϕ ◦

geometry

is AF Ω (spatial

disaggregation)
2. ϕ nbDamagedtrees : dom(S zone .geometry, S zone .
nbDamagedTrees) n → dom(S zone_agg .nbDam-
agedTrees) = φ nbTrees where:
φ ◦

nbDamagedTrees is Weighted Average on
surface
κ ◦

nbDamagedTrees = Average