Databases Reference
In-Depth Information
(iii)
|
G
K
|
=
|
G
K
|
(iv)
>
1)
is called a data mining generalization relation.
Directly from the above definition we get that the following theorem holds.
Theorem 3.
Let
∃
S
∈
G
K
(
|
S
|
≺
dm
be a relation defined in the Definition 10. The following
conditions hold.
(i) The relation
≺
dm
is transitive, and hence is a generalization relation in a
sense of the definition 1 of the Generalization Model
(ii)
≺
dm
is not reflexive and is not antisymmetric
2.4 Generalization Operators
Generalization operators by Definition 1, operate on the knowledge states,
preserving their generality, as defined by the generalization relation. I.e. a
partial function
G
:
K−→K
is called a generalization operator if for any
K,K
∈
domainG
G
(
K
)=
K
if and only if K
K
.
Generalization operators are designed to describe the action of different data
mining algorithms.
3 Data Mining Model
Data Mining process consists of two phases: preprocessing and data mining
proper. The Data Mining phase with its generalization operators is discussed
in detail in Sect. 4 and in its preliminary version in [14]. The preprocessing
operators and preprocessing phase as expressed within our Generalization
Model and are presented in Sect. 5 and in [13].
Data Mining Model defined below is a special case of the Generalization
Model, with generalization relation being data mining relation as defined in
Definition 10 and in which the generalization operators are defined as follows.
Definition 11.
An operator G ∈Gis called a
data mining generalization
operator
if and only if for any K,K
∈
domainG
G
(
K
)=
K
if and only if K
≺
dm
K
for some data mining generalization relation
≺
dm
(Definition 10)
Definition 12.
A
Data Mining Model
is a system
DM
=(
U,
K
,
G
dm
,
≺
dm
)
,
where the set
G
dm
is the set of data mining generalization operators.
The above Definition 11 defines a class of data mining operators. They are
discussed in detail in the next section.
