Association Rules

Association rule learning discovers relationships between variables in large databases, identifying frequent patterns, associations, and causal structures. It's widely used in market basket analysis, recommendation systems, and web usage mining.

Mathematical Foundations

Basic Terminology

• Itemset: A collection of items (e.g., butter)
• Transaction: A set of items purchased/used together
• Support: Frequency of itemset occurrence in dataset
• Confidence: Likelihood of consequent given antecedent
• Lift: Ratio of observed to expected frequency if independent

Association Rule Structure

Example: If butter → milk

Key Metrics

Support: Proportion of transactions containing the itemset

Confidence: Conditional probability of consequent given antecedent

Lift: Ratio of observed to expected support

Rust Implementation

Apriori Algorithm

The Apriori algorithm finds frequent itemsets by using the downward closure property: if an itemset is infrequent, all its supersets are also infrequent.

FP-Growth Algorithm

FP-Growth is more efficient than Apriori, avoiding candidate generation by using a compact tree structure.

Practical Applications

Market Basket Analysis Example

Recommendation System

Association rules provide powerful insights into item relationships and enable effective recommendation systems. The Rust implementation offers memory safety and performance benefits while maintaining the mathematical rigor of traditional association rule mining algorithms.