Clustering: Apriori

Introduction

Apriori is not a clustering algorithm in the usual sense. It is an association rule mining algorithm. It finds itemsets that frequently appear together and derives rules from them.

Classic use case: market-basket analysis.

Customers who buy bread and peanut butter also often buy jam.

Frequent Itemsets

An itemset is a set of items, such as:

{bread, peanut butter}

Support measures how often an itemset appears:

$$ support(A) = \frac{\text{transactions containing } A}{\text{all transactions}} $$

Apriori finds itemsets whose support exceeds a minimum threshold.

Apriori Principle

The key property:

If an itemset is frequent, all of its subsets must also be frequent.

This lets the algorithm prune the search space. If {bread, jam} is not frequent, then {bread, jam, milk} cannot be frequent.

Association Rules

A rule has the form:

A -> B

Confidence measures how often B appears when A appears:

$$ confidence(A \to B) = \frac{support(A \cup B)}{support(A)} $$

Lift compares the rule to chance:

$$ lift(A \to B) = \frac{confidence(A \to B)}{support(B)} $$

Lift greater than 1 suggests A and B appear together more often than expected if independent.

Practical Use

Apriori is useful for:

• Basket analysis.
• Product bundling.
• Recommendation rules.
• Event co-occurrence.
• Pattern discovery in transaction data.

Watch out:

• Too low support creates too many rules.
• High confidence can be misleading for very common items.
• Rules show association, not causation.
• Business usefulness matters more than rule count.

Closing

Apriori is a clear method for discovering frequent co-occurrence patterns. It is best used as exploratory analysis or as a simple rule-based recommendation ingredient.