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Analysis of Customer Behavior and Service Modeling Lecture 4: Association Market Basket Analysis 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 Rule Measures: Support and Confidence Customer buys both Find all the rules A C with minimum confidence and support Customer buys diaper – Support (s) probability that a transaction contains {A & C} – Confidence (c) conditional probability that a transaction having {A} also contains {C} Customer buys beer Transaction ID 2000 1000 4000 5000 Items Bought A,B,C A,C A,D B,E,F Let minimum support 50%, and minimum confidence 50%, we have A C (50%, 66.6%) C A (50%, 100%) Mining Association Rules: An Example Transaction ID 2000 1000 4000 5000 Items Bought A,B,C A,C A,D B,E,F Target: Min. support 50% Min. confidence 50% Frequent Itemset Support {A} 75% {B} 50% {C} 50% {A,C} 50% For rule A C: support = support({A, C}) = 50% confidence = support({A, C})/support({A}) = 66.6% 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 1 A 2 B 3 C 4 A, B 5 A, C 6 B, C 7 A, B, C 8 A, B, C An Example of Market Basket(1(2) Basic probabilities are below: (1) AB (2) (A, B) C LHS P(A) = 5/8 = 0.625 P(A,B) = 3/8 = 0.375 RHS P(B) = 5/8 = 0.625 P(C) = 5/8 = 0.625 Coverage LHS = 0.625 LHS = 0.375 Support P(A∩B) = 3/8 = 0.375 P((A,B)∩C)) = 2/8 =0.25 Confidence P(B|A)=0.375/0.625=0.6 P(C|(A,B))=0.25/0.375=0.7 Lift 0.375/(0.625*0.625)=0.96 0.25/(0.375*0.625)=1.07 Leverage 0.375 - 0.390 = -0.015 0.25 - 0.234 = 0.016 Lift 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). 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 – ③Two 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 http://www.rulequest.com 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 itl (identifier-item file) (item list file) 001, 001, 001, 002, 002, 002, 002, apples oranges bananas apples carrots lettuce 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 Data를 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 = 0.857 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 = 0.0258: the support is 0.0258 (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 = 0.042 support = 0.036: 18 cases satisfy both the LHS and the RHS – P((lettuce & carrots) ∩ tomatoes)) = 18/500 = 0.036 strength(confidence) = 0.857 – 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 = 0.0258: the support is 0.0258 (12.9 cases) greater than if there were no association – P(LHS ∩ RHS) – P(A)*P(B) = 0.036 – 0.042*0.244 = 0.0258