Just Enough R! by Roiger Richard J.;

Author:Roiger, Richard J.;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2020-11-15T00:00:00+00:00

If customers purchase bread, they also purchase milk.

If customers purchase milk and eggs, they also purchase cheese and bread.

If customers purchase milk, cheese, and eggs, they also purchase bread.

The first association tells us that a customer who purchases milk is also likely to purchase bread. The obvious question is “How likely will the event of a milk purchase lead to a bread purchase?” To answer this, each association rule has an associated confidence. For this rule, confidence is the conditional probability of a bread purchase given a milk purchase. Therefore, if a total of 10,000 customer transactions involve the purchase of milk, and 5000 of those same transactions also contain a bread purchase, the confidence of a bread purchase given a milk purchase is 5000/10,000 = 50%.

Now consider the second rule. Does this rule give us the same information as the first rule? The answer is no! With the first rule, the transaction domain consisted of all customers who had made a milk purchase. For this rule, the domain is the set of all customer transactions that show the purchase of a bread item. As an example, suppose we have a total of 20,000 customer transactions involving a bread purchase and of these, 5000 also involve a milk purchase. This gives us a confidence value for a milk purchase given a bread purchase of 25% vs. 50% for the first rule.

Although the third and fourth rules are more complex, the idea is the same. The confidence for the third rule tells us the likelihood of a purchase of both cheese and bread given a purchase of milk and eggs. The confidence for the fourth rule tells us the likelihood of a bread purchase given the purchase of milk, cheese, and eggs.

One important piece of information that a rule confidence value does not offer is the percent of all transactions containing the attribute values found in an association rule. This statistic is known as the supportfor a rule. Support is simply the minimum percentage of instances (transactions) in the database that contain all items listed in a specific association rule. In the next section, you will see how item sets use support to set limits on the total number of association rules for a given dataset.

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