public class AssociationRule
extends java.lang.Object
I = {i1, i2,..., in}
be a set of n binary attributes called items. Let
D = {t1, t2,..., tm}
be a set of transactions called the database. Each transaction in
D has an unique transaction ID and contains a subset
of the items in I. An association rule is defined
as an implication of the form X ⇒ Y
where X, Y ⊆ I and X ∩ Y = Ø.
The item sets X and Y are called
antecedent (left-hand-side or LHS) and consequent (right-hand-side or RHS)
of the rule, respectively.
The support supp(X) of an item
set X is defined as the proportion of transactions
in the database which contain the item set. Note that the support of
an association rule X ⇒ Y is supp(X ∪ Y).
The confidence of a rule is defined as
conf(X ⇒ Y) = supp(X ∪ Y) / supp(X).
Confidence can be interpreted as an estimate of the probability
P(Y | X), the probability of finding the RHS of the rule
in transactions under the condition that these transactions also contain
the LHS.
Lift is a measure of the performance of a targeting model
(association rule) at predicting or classifying cases as having
an enhanced response (with respect to the population as a whole),
measured against a random choice targeting model. A targeting model
is doing a good job if the response within the target is much better
than the average for the population as a whole. Lift is simply the ratio
of these values: target response divided by average response.
For an association rule X ⇒ Y, if the lift is equal
to 1, it means that X and Y are independent. If the lift is higher
than 1, it means that X and Y are positively correlated.
If the lift is lower than 1, it means that X and Y are negatively
correlated.
| Modifier and Type | Field and Description |
|---|---|
int[] |
antecedent
Antecedent itemset.
|
double |
confidence
The confidence value.
|
int[] |
consequent
Consequent itemset.
|
double |
leverage
The difference between the probability of the rule and the expected
probability if the items were statistically independent.
|
double |
lift
How many times more often antecedent and consequent occur together
than expected if they were statistically independent.
|
double |
support
The support value.
|
| Constructor and Description |
|---|
AssociationRule(int[] antecedent,
int[] consequent,
double support,
double confidence,
double lift,
double leverage)
Constructor.
|
| Modifier and Type | Method and Description |
|---|---|
boolean |
equals(java.lang.Object o) |
int |
hashCode() |
java.lang.String |
toString() |
public final int[] antecedent
public final int[] consequent
public final double support
public final double confidence
public final double lift
X ⇒ Y, if the lift is equal
to 1, it means that X and Y are independent. If the lift is higher
than 1, it means that X and Y are positively correlated.
If the lift is lower than 1, it means that X and Y are negatively
correlated.public final double leverage
public AssociationRule(int[] antecedent,
int[] consequent,
double support,
double confidence,
double lift,
double leverage)
antecedent - the antecedent itemset (LHS) of the association rule.consequent - the consequent itemset (RHS) of the association rule.support - the proportion of instances in the dataset that contain an itemset.confidence - the percentage of instances that contain the consequent
and antecedent together over the number of instances that
only contain the antecedent.lift - how many times more often antecedent and consequent occur together
than expected if they were statistically independent.leverage - the difference between the probability of the rule and the expected
probability if the items were statistically independent.