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In-Depth Information
3
Proposed Method
The proposed Consequent-based Association Rules Summarization (CARS) method
is simple. First, an association rule mining method with certain interestingness
threshold settings is applied to a dataset. If the support-and-confidence framework is
used, then its settings can abbreviated as
x
A
y
C, where
x
is the percentage of
antecedent support threshold, and
y
is the percentage of confidence threshold. The
rules generated are then grouped based by the consequent. Each group of rules that
has the same consequent
c
forms a
Rule Summary
(
RS
), which consists of the
following definitions:
•
Consequent Frequency:
Let
R
c
= {
r
1
,
r
2
, …,
r
m
} be a set of rules with the
same consequent
c
. That is,
∀
r
∈
R
c
:
c
∈
r
. The number of occurrences of
c
in
an
RS
is |
R
c
| =
m
. We name |
R
c
| as
Consequent Frequency
.
•
Antecedent Frequency:
Let
R
a
be a set of rules in
R
c
(i.e.,
R
a
⊆
R
c
), in which
each rule of
R
a
contains antecedent
a
. That is,
∀
r
∈
R
a
:
a
∈
r
. The number of
times antecedent
a
appears in
R
c
is |
R
a
|. We name |
R
a
| as Antecedent
Frequency.
•
Interestingness Metric Range (
f_range
):
Let
f
be a function for measuring
the interestingness of rules in an
RS
, then the range of
f
is [
f
min
,
f
max
], where
f
min
= min(
f
(
r
1
),
f
(
r
2
), …,
f
(
r
m
)), and
f
max
= max(
f
(
r
1
),
f
(
r
2
), …,
f
(
r
m
)). The function
f
can be antecedent support, rule confidence, lift, etc.
With the abovementioned definitions, an
RS
has the following abstract representation:
a
1
* |
R
a1
|,
a
2
* |
R
a2
|, …,
a
n
* |
R
an
| =>
c
*
m
with
f_range
: [
f
min
,
f
max
]
Supposed now a set of rules is generated from a dataset using
x
A
y
C, then rule
summaries can be derived from each set of rules that have common consequent(s).
Here we give an example of a rule summary from a set of two rules with the same
consequent, with
x
= 35%, and
y
= 80%.
Example 1.
Rule 1:
A, B => C
, with antecedent support = 42%, and confidence = 90%.
Rule 2:
B => C
, with antecedent support = 45%, and confidence = 92%.
Using the CARS approach, these two rules can be summarized as:
A*1, B*2 => C*2
With
support range
: [42%, 45%], and
confidence range
: [90%, 92%].
We now describe four properties of a Rule Summary using this example.
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