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It also proposes user-defined aggregation func-
tions for each attribute of the geographic object
representing the aggregated measure. GeoCube
also provides an algebra that redefines common
OLAP operators.
•
If F does not exist, ti
i
=
á
val(ai)
1
),…val(a
n
)
ñ
where val(ai)
i
)
∈
dom(a
i
)
F
permits to model derived measures and/or
dimension attributes.
Data Model
Definition. (Geographic Entity Schema).
An
Entity Schema
S
e
is a
Geographic Entity
Schema
if the domain of one attribute is a set of
spatial objects.
Example 1.
In the case study presented previ-
ously, the geographic measure representing the
zones is S
zone
= ágeometry, nbDamagedTrees, f
area
ñ
where f
area
: dom(geometry) → N is a function to
calculate the area of a zone. An instance of S
zone
is
ápt01, 20, 110ñ (Zone A) (Figure 2).
Entities
are organized in hierarchies thanks to
the concepts of
Hierarchy Schema
and
Hierarchy
Instance
. A level of a hierarchy is an
Entity Schema
and a member is an
Entity Instance
. The
Hierarchy
Schema
organizes levels into a lattice. Thanks to
the
Hierarchy Instance
, the members' levels are
organized in a tree structure. The root is an instance
of the
Entity Schema
which represents the top level
of the lattice represented by the
Hierarchy Schema
.
Leafs are the instances of the
Entity Schema
which
represents the bottom level of the lattice.
This definition allows modeling non-balanced
and non-strict hierarchies, which are necessary for
spatio-multidimensional applications (Malinowski
& Zimányi, 2005).
The main concepts of multidimensional data model
are:
Entity
,
Hierarchy
and
Base Cube
. The con-
cepts of
Entity Schema
and
Entity Instance
permit
to represent indifferently the data of the analysis
universe: dimension members and measures. An
Entity is a set of attributes and functions used to
represent derived attributes (data calculated using
other data). Derived attributes are necessary to
model metric attributes (i.e. area, perimeter, etc.)
of geographic objects.
Entity Schemas
and their instances are orga-
nized into hierarchies (
Hierarchy Schema
and
Hierarchy Instance
). The
Base Cube
represents
the facts table.
In what follows, we only provide the defini-
tions that are necessary to describe the framework
we propose.
Definitions. (Entity Schema and Entity
Instance).
An Entity Schema S
e
is a tuple áa
1
, …a
n
, [F]
ñ where:
•
a
i
is an attribute defined on a domain
dom(a
i
)
Definition. (Hierarchy).
A Hierarchy Schema is a tuple H
h
= áL
h
,
⌊
h
,
⌈
h
,
⇞
h
ñ where:
•
F, if it exists, is a tuple
á
f
1
,…f
m
ñ
where f
i
is a
function defined on a sub-set of attributes
a
r
, …a
k
.
• L
h
is a set of Entity Schemas,
•
⌊
h
and
⌈
h
are two Entity Schema and
⌈
h
con-
tains one instance ('all'),
•
⇞
h
is a partial order defined on the levels
of the hierarchy (L
h
∪ ⌊
h
∪ ⌈
h
) and
⇞
h
is a
lattice where
⌊
h
and
⌈
h
are respectively the
bottom and the top levels of the order.
An Instance of an Entity Schema S
e
is a tuple
t
i
such as
•
If F exists then ti
i
=
á
val(ai)
1
), val(a
n
),
val(b
1
),…val(b
m
)
ñ
where val(ai)
i
)
∈
dom(a
i
)
and val(b
j
) = f
j
(val(a
r
),…val(a
k
))
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