Association Rules Carissa Wang February 23, 2010

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

Definition X => Y X = {x 1, x 2, …, x n } Y = {y 1, y 2, …, y n } x i and y j are distinct items for all i and all j X is the left-hand-side (LHS) Y is the right-hand-side (RHS)

Example Transaction IDItems Bought 1Milk, bread, cookies, juice 2Milk, juice 3Milk, eggs 4Bread, cookies, coffee

Measuring the rule Support  Frequency of an item set occurs in the database  Item set – LHS  RHS Confidence  Probability of LHS => RHS

Support Rules  Milk => juice  Bread => juice {milk, juice}  2 / 4 = 0.50 {bread, juice}  1 / 4 = 0.25 Transaction ID Items Bought 1Milk, bread, cookies, juice 2Milk, juice 3Milk, eggs 4Bread, cookies, coffee

Confidence Rules  Milk => juice  Bread => juice Milk => juice  0.50 / 0.75 = 0.67 Bread => juice  0.25 / 0.50 = 0.50 Transactio n ID Items Bought 1Milk, bread, cookies, juice 2Milk, juice 3Milk, eggs 4Bread, cookies, coffee

What these numbers mean Support  High – LHS => RHS  Low – not enough evidence of LHS => RHS Confidence  High – given condition LHS, RHS will occur  Low – RHS does not occur consistently

Other measures of association rule Lift Conviction All – confidence Collective strength Leverage

Algorithm to generate association rule Apriori Algorithm Eclat Algorithm Frequent Pattern Growth Algorithm One Attribute Rule Zero Attribute Rule

Apriori Algorithm Database with large transactions Breadth-first search Two properties  Downward closure  Antimonotonicity

Apriori Property Downward Closure  Subset of large item set is also large Antimonotonicity  Superset of small item set is small

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

How Apriori algorithm works ItemSupport ItemSupport {1,2}3 {1,3}2 {1,4}3 {2,3}4 {2,4}5 {3,4}3 ItemSupport {1,2,4}3 {2,3,4}3 Min Frequency = 3

Applications Web usage mining Intrusion detection Bioinformatics

Reference Apriori algorithm, Wikipedia  Fundamentals of Database Systems, 5 th ed, Elmasri and Navathe Association rule learning, Wikipedia 