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 a 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 itemset.
    final double
    The confidence value.
    final int[]
    Consequent itemset.
    final double
    The difference between the probability of the rule and the expected probability if the items were statistically independent.
    final double
    How many times more often antecedent and consequent occur together than expected if they were statistically independent.
    final double
    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
     
    int
     
     

    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