Database Reference
In-Depth Information
Multidimensional Query Model
We call
Entity Schema levels
(
L(H
h
)
) the enti-
ties belonging to the set {L
h
∪
⌊
h
∪
⌈
h
}
An Instance of a Hierarchy H
h
is a partial order
↑
h
defined on L(H
h
), such as:
• if ti
i
↑
h
t
j
then S
i
⇞
h S
j
, where t
i
∈
I(S
i
) and t
j
∈
I(S
j
)
•
∀
t
i
not belonging to the top level, then
∃
t
j
such as t
i
↑h t
j
•
∀
t
i
not belonging to the bottom level,
∃
t
j
such as t
j
↑h t
i
Base Cube represents the basic cuboid, which is
represented by measures values associated with
the most detailed levels of all hierarchies. These
measures are not aggregated. Then, in order to
represent a multidimensional query (i.e. cuboid),
we introduce the concepts of
Aggregation Mode
and
View
. A multidimensional query defines the
dimension levels used (e.g. “Type” and “Year”),
the (geographic) object used as measure (“Zone”)
and a set of aggregation functions (
Aggregation
Mode
) to aggregate its attributes (e.g. union for
geometry and sum for number of trees) (Figure
7). For simplicity, we provide only the definition
of the
Aggregation Mode
and we give a example
of
View
.
Aggregation Mode
defines a function for
each non-derived attribute of the
(Geographic)
Entity
representing the measure. The result of
the aggregation is another
(Geographic) Entity
whose attributes values are calculated using these
functions.
Schema and data of the spatio-multidimension-
al application are represented by
Base Cube
.
Base
Cube Schema
defines dimensions (Hierarchies)
and measures (e.g. the spatio-multidimensional
application schema of Figure 1). The instance of
the
Base Cube
represents facts table data (e.g. data
of Figure 2). In our approach, dimensions and mea-
sures are (geographic) objects, for example phe-
nomena and zones. Then, our model must define
measures in the same way as dimensions levels.
Following the approach of Vassiliadis (1998), we
define a
Base Cube
as a tuple of
Hierarchies
and
a boolean function which represents the tuples
of the facts table. Here, the bottom levels of the
hierarchies are (geographic) objects. They can be
used as dimensions and measures. This definition
allows defining measures as (geographic) objects,
and not as numerical value.
Example 2.
The multidimensional model of
figure 1 is represented by the Base Cube Schema
BC
naturalrisks
= áH
natural_phenomena
, H
time,
H
zone,
δñ where
H
natural_phenomena
, H
time
and H
zone
are the hierarchies
representing the phenomena, time and zones. δ:
I(S
phenomen
)×I(S
day
)×I(S
zone
) is a boolean function
defined on the bottom levels of the hierarchies.
The instance of BC
naturalrisks
represents the facts
table (Figure 2).
In this application, each bottom level of a
hierarchy (object and/or geographic object) can
be used as measure.
Definition. (Aggregation Mode).
An Aggregation Mode Θ
k
is a tuple áS
a
, S
b
,
Φñ where:
•
S
a
is an Entity Schema
á
a
1
,…a
m
, [F
a
]
ñ (the
detailed measure)
•
S
b
is an Entity Schema
á
b
1
,…b
p
, [F
b
]
ñ (the
aggregated measure)
•
Φ a set of p ad-hoc aggregation functions
ϕ
i
An
Aggregation Mode
defined on geographic
objects (geographic measures) is called
Geo-
graphic Aggregation Mode
.
Definition. (Geographic Aggregation
Mode)
An Aggregation Mode Θ
k
=áS
a
, S
b
, Φñ is a
Geographic Aggregation Mode if S
a
and S
b
are
Geographic Entity Schemas.
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