Apriori Principle and Its Significance

The Apriori Principle is a data mining concept that if an itemset is frequent, then all of its subsets must also be frequent.
This principle is used in association rule mining to reduce the number of itemsets that need to be examined to find frequent itemsets in a dataset.

Description

• Frequent Itemset: An itemset is considered frequent if it meets a minimum support threshold, which is the proportion of transactions in which the itemset appears;
• Subset Property: The Apriori Principle states that if an itemset is frequent, then all of its subsets must also be frequent. This property is derived from the definition of support: the support of an itemset cannot exceed the support of its subsets;
• Pruning: By leveraging the subset property, we can prune the search space by eliminating candidate itemsets that contain subsets that are infrequent. This reduces the computational complexity of finding frequent itemsets in large datasets.

Example

Assume we have the dataset with the following frequent itemset:
{milk, bread, eggs}.

According to the Apriori Principle, we can infer that the following subsets must also be frequent:

• {milk, bread};
• {milk, eggs};
• {bread, eggs};
• {milk};
• {bread};
• {eggs}.