3.Mining Association Rules in Large Database 3.1 Market Basket Analysis:Example for Association Rule Mining 1.A typical example of association rule mining is market basket analysis. This process analyzes customer buying habits by finding associations between the different items that customer place in their”shopping baskets”

milk bread milk bread sugar eggs sugar eggs butter customer1 customer2 customer3 Association rules:milk  sugar? 2.formalization Idi1i2i3i4 1××× 2×× 3××× 4××

Rules:i1===>i4 Support=50%,confidence=100% If a rule concerns associations between the presence or absence of items,it is a Boolean association rule.

3.2 Basic Concepts Let I={i1,i2,i3….in} be a set of items,D be a set of transactions,each transaction T is a set of items such that T ≦ I. each transaction is associated with an identifier,called TID. Example: T1={i1,i3,i4},TID=1 An association rule is an implication of the form A  B,where A ≦ I,B ≦ I,and A∩B= Φ

The rules A=>B holds in the transaction set D with support s,where s is the percentage of transaction in D that contain A ∪ B. with confidence c is the the percentage of transaction in D containing A that also contain B. support(A=>B)=(count of contain A and B)/ (count of D)×100% confidence(A=>B)=(count of contain A and B)/(count of A) × 100  P(B|A)

Example: support(i1=>i4)=50% confidence(i1=>i4)=100% TIDi1i2i3i4 1××× 2×× 3××× 4××

Rules that satisfy following condition: support(A=>B)>=min_sup confidence(A=>B)>=min_conf Are called strong. A set of items is referred to as an itemset,{i1,i3}.the occurrence frequency of an itemset is the number of transactions that contain the itemset,simply,count of itemset. {i1,i3}—itemset,count of itemset is 1.

If an itemset satisfies minimum support count,then it is a frequent itemset. where minimum support count= min_sup×count of D Example: minimum support count=2 {i1},{i2},{i3},{i4},{i1,i4},{i3,i4} is frequent itemset.

Association rule mining is a two-step process 1.Find all frequent itemsets:By definition,each of these itemsets will occur at least as frequently as a pre-determined minimum support count. 2.Generate strong association rules from the frequent itemsets: By definition,these rules must satisfy minimum support and minimum confidence.

3.3 the Apriori algorithm:find frequent itemsets Apriori property:all nonempty subsets of a frequent itemset must also be frequent. Step 1:scanning each record(transaction),counting of each item. Step 2:the minimum support count are frequent by definition,to determine L1.

Step 3:joining L1 and L1,generate a set of candidate(C2),A scan of database to determine the count of each candidate in C2 would result in the determination of L2. Step 4:Repeat step 3 until Ln is empty,Ln-1 is frequent itemset.

Example: min support is 60%=2.4(support count) min confidence is 80% TIDList of item_IDs T001 T002 T003 T004 i1,i2,i4,i6 i1,i2,i3,i4,i5 i1,i2,i3,i5 i1,i2,i4

itemsetcount {i1} {i2} {i3} {i4} {i5} {i6} itemsetcount {i1} {i2} {i4} C1 L1

itemsetcount {i1,i2} {i1,i4} {i2,i4} itemsetcount {i1,i2} {i1,i4} {i2,i4} itermsetcount {i1,i2,i4}3 C2 L2 C3 L3

3.4 Generating Association Rules from Frequent Itemset Once the frequent itemsets from transactions in a database D have been found,association rules can be generated as follows: For each frequent itemset l,generate all nonempty subsets of l. For every nonempty subsets s of l,output the rule “s=>(l-s)”. confidence{s=>(l-s)}=P(l-s|s)=sup- cont(l)/sup-cont(s)

Example:l={i1,i2,i4} Nonempty subset of l: {i1,i2},{i1,i4},{i2,i4},{i1},{i2},{i4} Rule and confidence: i1 Λ i2=>i4,confidence=3/4=75% i1 Λ i4=>i2, confidence=3/3=100%>80% i2 Λ i4=>i1, confidence=3/3=100%>80% i1=>i2 Λ i4, confidence=3/4=75% i2=>i1 Λ i4, confidence=3/4=75% i4=>i1 Λ i2, confidence=3/3=100%>80%

Exercises: TIDList of item_IDs T100 T200 T300 T400 T500 T600 T700 T800 T900 I1,I2,I5 I2,I4 I2,I3 I1,I2,I4 I1,I3 I2,I3 I1,I3 I1,I2,I3,I5 I1,I2,I3 Min_sup =22% Min_conf= 70%