1. Association Rule Mining Data Mining and Knowledge Discovery Prof. Carolina Ruiz and Weiyang Lin Department of Computer Science Worcester Polytechnic Institute

2. Sample Applications Commercial Market basket analysis cross-marketing attached mailing store layout, catalog design customer segmentation based on buying patterns Scientific Genetic analysis Analysis of medical data Industrial

3. Transactions and Assoc. Rules Association Rule: a → c confidence: 66% (percentage of transactions which contain a also contain c.) = P(c | a) support: 50% (percentage of transactions contain both a and c.) = P(a & c)

4. Association Rules - Intuition Given a set of transactions where each transaction is a set of items Find all rules X → Y that correlate the presence of one set of items X with another set of items Y - Example: 98% of people who purchase diapers and baby food also buy beer. - Any number of items in the antecedent and in the consequent of a rule. - Possible to specify constraints on rules

5. Mining Association Rules Problem Statement Given: a set of transactions (each transaction is a set of items) user-specified minimum support user-specified minimum confidence Find: all association rules that have support and confidence greater than or equal to the user-specified minimum support and minimum confidence

6. Naïve Procedure to mine rules List all the subsets of the set of items For each subset Split the subset into two parts (one for the antecedent and one for the consequent of the rule Compute the support of the rule Compute the confidence of the rule IF support and confidence are no lower than user- specified min. support and confident THEN output the rule Complexity: Let n be the number of items. The number of rules naively considered is: n i-1  [( i n )  ( k i )] i=2 k=1 n  [( i n )  (2 i -2) ] i=2 = 3 n – 2 (n+1) + 1

7. The Apriori Algorithm 1. Find all frequent itemsets: sets of items whose support is greater than or equal the user-specified minimum support. 2. Generate the desired rules: if {a, b, c, d} and {a, b} are frequent itemsets, then compute the ratio conf (a & b → c & d) = P(c & d | a & b) = P( a & b & c & d)/P(a & b) = support({a, b, c, d})/support({a, b}). If conf >= mincoff, then add rule a & b → c & d

8. The Apriori Algorithm — Example slide taken from J. Han & M. Kamber’s Data Mining book Database D Scan D C1C1 L2L2 L3L3 C3C3 L1L1 C2C2 C2C2 Min. supp = 50%, I.e. min support count = 2

9. Apriori Principle Key observation: Every subset of a frequent itemset is also a frequent itemset Or equivalently, The support of an itemset is greater than or equal to the support of any superset of the itemset

10. Apriori - Compute Frequent Itemsets Making multiple passes over the data for pass k {candidate generation: C k := L k-1 joined with L k-1 ; support counting in C k; L k := All candidates in C k with minimum support; } terminate when L k == or C k+1 == Frequent-Itemsets = k L k L k - Set of frequent itemsets of size k. (those with minsup) C k - Set of candidate itemsets of size k. (potentially frequent itemsets)

11. Apriori – Generating rules For each frequent itemset: - Generate the desired rules: if {a, b, c, d} and {a, b} are frequent itemsets, then compute the ratio conf (a & b → c & d) = support({a, b, c, d})/support({a, b}). If conf >= mincoff, then add rule a & b → c & d