Lecture 4: Association Market Basket Analysis Analysis of Customer Behavior and Service Modeling

What Is Association Mining?  Association rule mining: – Finding frequent patterns, associations, correlations, or causal structures among sets of items or objects in transaction databases, relational databases, and other information repositories.  Applications: – Market basket analysis, cross-marketing, catalog design, loss- leader analysis, clustering, classification, etc.  Examples: – Rule form: “ Body  Head [support, confidence] ” buys(x, “ diapers ” )  buys(x, “ beers ” ) [0.5%, 60%] major(x, “ CS ” ) ^ takes(x, “ DB ” )  grade(x, “ A ” ) [1%, 75%]

Support and Confidence  Support –Percent of samples contain both A and B –support(A  B) = P(A ∩ B)  Confidence –Percent of A samples also containing B –confidence(A  B) = P(B|A)  Example –computer  financial_management_software [support = 2%, confidence = 60%]

Association Rules: Basic Concepts  Given: (1) database of transactions, (2) each transaction is a list of items (purchased by a customer in a visit)  Find: all rules that correlate the presence of one set of items with that of another set of items –e.g., 98% of people who purchase tires and auto accessories also get automotive services done  Applications –Home Electronics - What other products should the store stocks up? –Retailing – Shelf design, promotion structuring, direct marketing

 Find all the rules A  C with minimum confidence and support –Support (s) probability that a transaction contains {A & C} –Confidence (c) conditional probability that a transaction having {A} also contains {C} Let minimum support 50%, and minimum confidence 50%, we have A  C (50%, 66.6%) C  A (50%, 100%) Customer buys diaper Customer buys both Customer buys beer Rule Measures: Support and Confidence

For rule A  C: support = support({A, C}) = 50% confidence = support({A, C})/support({A}) = 66.6% Target: Min. support 50% Min. confidence 50% Mining Association Rules: An Example

An Example of Market Basket(1)  There are 8 transactions on three items on A (Apple), B (Banana), C (Carrot).  Check associations for below two cases. (1) A  B (2) (A, B)  C #Basket 1A 2B 3C 4A, B 5A, C 6B, C 7A, B, C 8

An Example of Market Basket(1(2)  Basic probabilities are below: (1) A  B(2) (A, B)  C LHSP(A) = 5/8 = 0.625P(A,B) = 3/8 = RHSP(B) = 5/8 = 0.625P(C) = 5/8 = CoverageLHS = 0.625LHS = SupportP(A∩B) = 3/8 = 0.375P((A,B)∩C)) = 2/8 =0.25 ConfidenceP(B|A)=0.375/0.625=0.6P(C|(A,B))=0.25/0.375=0.7 Lift0.375/(0.625*0.625)= /(0.375*0.625)=1.07 Leverage = = 0.016

 What are good association rules? (How to interpret them?) –If lift is close to 1, it means there is no association between two items (sets). –If lift is greater than 1, it means there is a positive association between two items (sets). –If lift is less than 1, it means there is a negative association between two items (sets). Lift

Leverage –Leverage = P(A∩B) - P(A)*P(B), it has three types ① Leverage > 0 ② Leverage = 0 ③ Leverage < 0 – ① Two items (sets) are positively associated – ② Two items (sets) are independent – ③ Two items (sets) are negatively associated

Lab on Association Rules(1)  SPSS Clementine, SAS Enterprise Miner have association rules softwares.  This exercise uses Magnum Opus.  Go to and download Magnum Opus evaluation version (  click)

 After you install the problem, you can see below initial screen. From menu, choose File – Import Data (Ctrl – O).

 Demo Data sets are already there. Magnum Opus has two types of data sets available: (transaction data: *.idi, *.itl) and (attribute-value data: *.data, *.nam)  Data format has below two types:(*.idi, *.itl). idi (identifier-item file) itl (item list file) 001, apples 001, oranges 001, bananas 002, apples 002, carrots 002, lettuce 002, tomatoes apples, oranges, bananas apples, carrots, lettuce, tomatoes

 If you open tutorial.idi using note pad, you can see the file inside as left.  The example left has 5 transactions (baskets)

 File – Import Data, or click. click Tutorial.idi  Check Identifier – item file and click Next >.

 Click Yes and click Next > …  click Next > …

 Click Next > …  What percentage of whole file you want to use? Type 50% and click Next > …

 click Import Data 를 클릭  Then, you can see a screen like below left.

 Set things as they are. –Search by: LIFT –Minimum lift: 1 –Maximum no. of rules: 10  Click GO

 Results are saved in tutorial.out file.  Below are rules derived: lettuce & carrots are associated with tomatoes with strength = coverage = 0.042: 21 cases satisfy the LHS support = 0.036: 18 cases satisfy both the LHS and the RHS lift 3.51: the strength is 3.51 times greater than the strength if there were no association leverage = : the support is (12.9 cases) greater than if there were no association

 lettuce & carrots  tomatoes –When Lettuce and carrots are purchase then they buy tomatoes –coverage = 0.042: 21 cases satisfy the LHS –LHS(lettuce & carrots) = 21/500 =  support = 0.036: 18 cases satisfy both the LHS and the RHS –P((lettuce & carrots) ∩ tomatoes)) = 18/500 =  strength(confidence) = –P(support|LHS)= 18/21 = 0.036/0.042 = 0.857

 lift 3.51: the strength is 3.51 times greater than the strength if there were no association – 즉, (18/21)/(122/500) = 3.51  leverage = : the support is (12.9 cases) greater than if there were no association –P(LHS ∩ RHS) – P(A)*P(B) = – 0.042*0.244 =