public class AssociationRule
extends java.lang.Object
I = {i_{1}, i_{2},..., i_{n}}
be a set of n
binary attributes called items. Let
D = {t_{1}, t_{2},..., t_{m}}
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 (lefthandside or LHS) and consequent (righthandside 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.