Support, Confidence, and Lift Measures

Support, confidence, and lift are key measures that play a crucial role in evaluating the significance and strength of item relationships in ARM. Understanding these measures is essential for interpreting the results of association rule mining and deriving actionable insights from the data.

Support

Support is a metric used in association rule mining to measure the frequency of occurrence of an itemset in a dataset. It indicates how often a particular combination of items appears together in transactions relative to the total number of transactions.
Support for an itemset X is calculated as the ratio of the number of transactions containing all the items in X to the total number of transactions in the dataset:

Support is used to identify frequent itemsets: itemsets with high support values represent significant patterns in the dataset and are considered potential candidates for generating association rules.

Note

By using support we can answer the following question: How frequently does the itemset X occur in the dataset?

Confidence

Confidence is a metric used in association rule mining to measure the reliability or strength of a discovered association between two items in a dataset. It indicates the likelihood that an item Y is purchased when item X is purchased, representing the conditional probability of the consequent given the antecedent. Confidence for an association rule X -> Y is calculated as the ratio of the number of transactions containing both X and Y to the number of transactions containing X:

Confidence is used to assess the strength and reliability of association rules generated from frequent itemsets. High-confidence rules indicate that the presence of the antecedent significantly influences the occurrence of the consequent, making the rule more actionable and reliable.

Note

By using confidence we can answer the following question: Given the occurrence of itemset X, how likely is it that itemset Y also occurs?

Lift

Lift is a metric used in association rule mining to measure the strength of association between items in a rule compared to what would be expected if they were independent. It quantifies how much more likely the consequent is to occur when the antecedent is present, relative to its individual occurrence.
Lift for an association rule X -> Y is calculated as the ratio of the observed support of the itemset X and Y to the expected support under independence:

Lift interpretation

1. Lift values greater than 1 indicate that the antecedent and consequent occur together more often than if they were independent. This suggests a positive association between the items, meaning that the presence of the antecedent increases the likelihood of the consequent;
2. Lift values less than 1 indicate a negative or inverse association. In this case, the presence of the antecedent decreases the likelihood of the consequent;
3. Lift values equal to 1 indicate independence, meaning that the occurrence of the antecedent has no effect on the occurrence of the consequent. The items are independent of each other.

Note

By using lift we can answer the following question: How much more frequently do items X and Y co-occur together compared to what would be expected if their occurrences were independent?