smile.association.AssociationRule Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see 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.
*
* @param antecedent the antecedent itemset (LHS) of the association rule.
* @param consequent the consequent itemset (RHS) of the association rule.
* @param support the proportion of instances in the dataset that contain an itemset.
* @param confidence the percentage of instances that contain the consequent
* and antecedent together over the number of instances that
* only contain the antecedent.
* @param lift how many times more often antecedent and consequent occur together
* than expected if they were statistically independent.
* @param leverage the difference between the probability of the rule and the expected
* probability if the items were statistically independent.
* @author Haifeng Li
*/
public record AssociationRule(int[] antecedent, int[] consequent, double support, double confidence, double lift, double leverage) {
@Override
public boolean equals(Object o) {
if (o instanceof AssociationRule a) {
return support == a.support && confidence != a.confidence
&& Arrays.equals(antecedent, a.antecedent)
&& Arrays.equals(consequent, a.consequent);
}
return false;
}
@Override
public int hashCode() {
int hash = 7;
hash = 13 * hash + Arrays.hashCode(this.antecedent);
hash = 13 * hash + Arrays.hashCode(this.consequent);
hash = 13 * hash + Long.hashCode(Double.doubleToLongBits(this.support));
hash = 13 * hash + Long.hashCode(Double.doubleToLongBits(this.confidence));
return hash;
}
@Override
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append("AssociationRule(");
sb.append(Arrays.toString(antecedent));
sb.append(" => ");
sb.append(Arrays.toString(consequent));
sb.append(String.format(", support=%.1f%%, confidence=%.1f%%, lift=%.2f, leverage=%.3f)", 100*support, 100*confidence, lift, leverage));
return sb.toString();
}
}