Information Technology Reference
In-Depth Information
Beacause the expected confidence is the probability of the occurrence of set
B
in
all transactions and the confidence is the probability of the occurrence of set
B
in
the transactions which set
is presented. Then the ratio of confidence to the
expected confidence reflects the change of probability of the occurrence of set
A
B
when the precondition “the occurrence of set
A
” is added. The lift between the
occurrence of
A
and
B
can be measured by computing
)
P A
∪
B
lift A B
,
)
=
(12.2)
P A P B
(
)
(
)
In the above example, the lift is 70
/20
=3.5.
Let
P
(
A
) be the probability of the occurrence of itemset
A
,
P
(
B|A
) be the
probability of the occurrence of itemset
B
when itemset
A
occurs, then the above
four parameters can be expressed as Table 12.1.
Confidence is a precise measure for an association rule. Support is an
measure for the importance of a association rule. Support stands for the
importance of a rule and the more the support is, the more important the rule is.
There are rules which are with high confidence but low support, which means
that the rule is neither important nor practical.
Table 12.1. Formula of the four parameters
Name
Description
Formula
the probability of the occurrence of itemset
B
when itemset
A
is occurred
Confidence
P
(
B|A
)
the probability of the occurrence of both
itemset
A
and itemset
B
Support
P
(
A
∪
B
)
Expected Confidence
the probability of the occurrence of itemset
B
P
(
B
)
the ratio of confidence to the expected
confidence
Lift
P
(
B|A
)/
P
(
B
)
Expected confidence describes the support of itemset
B
where there is no
influence from itemset
A
. Lift describes the influence of itemset
A
on itemset
B
.
A great lift shows a great influence of itemset
. Generally, the lift
is often greater than 1 when the rule is practical for applications. Only when the
confidence is greater than expected confidence, then the presence of
A
on itemset
B
A
has
promoted effect on the presence of
and it shows itemsets A and B are related
on some grade. If the lift is less than 1, it shows that the rule has no meaning.
B
