Lecture 2 - Frequent Itemset Mining and Association Rules

Key Concepts

• Goal: Find relationships among items frequently purchased together.
• Applications: Market basket analysis, recommendation systems, fraud detection.

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Definitions

• Item: e.g., milk, bread, beer.
• Basket/Transaction: Set of items bought together.
• Support: Number (or fraction) of baskets containing an itemset.
• Frequent Itemset: Appears in at least s baskets.

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Association Rules

• Form: {X} → {Y} meaning “if X is bought, Y is likely to be bought.”
• Confidence:
  $(\text{conf}(X\to Y)=\frac{\text{support}(X\cup Y)}{\text{support}(X)})$
• Interest:
  $(\text{interest}=\text{conf}(X\to Y)-P(Y))$

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Compact Representations

• Maximal Itemsets: No frequent supersets exist.
• Closed Itemsets: Superset has the same support count.

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Algorithms

1. Brute-Force

• Generate all possible item combinations.
• Count frequencies (expensive for large data).

2. A-Priori Algorithm

• Idea: Downward closure property. - All subsets of a frequent itemset must also be frequent.
• Uses multiple passes:
  1. Find frequent individual items (L1).
  2. Generate candidate pairs (C2) from L1.
  3. Count pairs across baskets.
  4. Continue for k-tuples until no frequent sets found.

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Example

• Baskets:
  {milk, bread, beer}, {milk, diaper, beer}, {bread, milk, coke}, etc.
• Frequent sets (s ≥ 3): {milk}, {beer}, {milk, beer} etc.

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Storage & Efficiency

• Naïve pair counting → (O(n^2)) memory.
• Triangular matrix or hashes can save memory.
• A-Priori greatly reduces unnecessary counting.

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Summary

• Identify strong correlations between items (association rules).
• Optimize computation using frequency thresholds.
• A-Priori = cornerstone algorithm for large-scale data mining.