Association Rules

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Association Rules

• Carissa Wang
• February 23, 2010

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What is Association Rule

• In data mining, it is a method for discovering
  relations between different sets of items in a
  large database.
• Database
• A large collection of transactions
• Example - Market basket database

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Definition

• X gt Y
• X x1, x2, , xn
• Y y1, y2, , yn
• xi and yj are distinct items for all i and all j
• X is the left-hand-side (LHS)
• Y is the right-hand-side (RHS)

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Example
Transaction ID Items Bought
1 Milk, bread, cookies, juice
2 Milk, juice
3 Milk, eggs
4 Bread, cookies, coffee
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Measuring the rule

• Support
• Frequency of an item set occurs in the database
• Item set LHS ? RHS
• Confidence
• Probability of LHS gt RHS

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Support

• Rules
• Milk gt juice
• Bread gt juice
• milk, juice
• 2 / 4 0.50
• bread, juice
• 1 / 4 0.25

Transaction ID Items Bought
1 Milk, bread, cookies, juice
2 Milk, juice
3 Milk, eggs
4 Bread, cookies, coffee
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Confidence

• Rules
• Milk gt juice
• Bread gt juice
• Milk gt juice
• 0.50 / 0.75 0.67
• Bread gt juice
• 0.25 / 0.50 0.50

Transaction ID Items Bought
1 Milk, bread, cookies, juice
2 Milk, juice
3 Milk, eggs
4 Bread, cookies, coffee
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What these numbers mean

• Support
• High LHS gt RHS
• Low not enough evidence of LHS gt RHS
• Confidence
• High given condition LHS, RHS will occur
• Low RHS does not occur consistently

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Other measures of association rule

• Lift
• Conviction
• All confidence
• Collective strength
• Leverage

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Algorithm to generate association rule

• Apriori Algorithm
• Eclat Algorithm
• Frequent Pattern Growth Algorithm
• One Attribute Rule
• Zero Attribute Rule

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Apriori Algorithm

• Database with large transactions
• Breadth-first search
• Two properties
• Downward closure
• Antimonotonicity

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Apriori Property

• Downward Closure
• Subset of large item set is also large
• Antimonotonicity
• Superset of small item set is small

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How Apriori algorithm works

• Find subsets with minimum frequency of in the
  given transactions
• Extend the subsets by one item and keep the
  subsets that meet the minimum frequency
• Repeat last step until no frequent superset

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How Apriori algorithm works
Item Support
1,2 3
1,3 2
1,4 3
2,3 4
2,4 5
3,4 3
Min Frequency 3
Item Support
1 3
2 6
3 4
4 5
Item Support
1,2,4 3
2,3,4 3
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Applications

• Web usage mining
• Intrusion detection
• Bioinformatics

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Reference

• Apriori algorithm, Wikipedia
• http//en.wikipedia.org/wiki/Apriori_algorithm
• Fundamentals of Database Systems, 5th ed, Elmasri
  and Navathe
• Association rule learning, Wikipedia
• http//en.wikipedia.org/wiki/Association_rules