Package smile.association

Class AssociationRule

java.lang.Object

smile.association.AssociationRule

public class AssociationRule
extends Object

Association rule object. Let 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.

Field Summary

Fields

Modifier and Type	Field	Description
final int[]	antecedent	Antecedent itemset.
final double	confidence	The confidence value.
final int[]	consequent	Consequent itemset.
final double	leverage	The difference between the probability of the rule and the expected probability if the items were statistically independent.
final double	lift	How many times more often antecedent and consequent occur together than expected if they were statistically independent.
final double	support	The support value.

Constructor Summary

Constructors

Constructor	Description
AssociationRule(int[] antecedent, int[] consequent, double support, double confidence, double lift, double leverage)	Constructor.

Method Summary

Modifier and Type	Method	Description
boolean	equals(Object o)
int	hashCode()
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

antecedent

public final int[] antecedent

Antecedent itemset.

consequent

public final int[] consequent

Consequent itemset.

support

public final double support

The support value. The support supp(X) of an itemset X is defined as the proportion of transactions in the database which contain the itemset.

confidence

public final double confidence

The confidence value. The confidence of a rule is defined 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

public final double lift

How many times more often antecedent and consequent occur together than expected if they were statistically independent. 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.

leverage

public final double leverage

The difference between the probability of the rule and the expected probability if the items were statistically independent.

Constructor Details

AssociationRule

public AssociationRule(int[] antecedent,
 int[] consequent,
 double support,
 double confidence,
 double lift,
 double leverage)

Constructor.

Parameters:

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.

Method Details

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

toString

public String toString()

Overrides:

toString in class Object