I. 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 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

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 # Basket 1 A 2 B 3 C 4 A, B 5 A, C 6 B, C 7 A, B, C 8

An Example of Market Basket(1(2) Basic probabilities are below: (1) AB Coverage 5/8 = 0.625 Support P(A∩B) = 3/8 = 0.375 Confidence P(B|A)=0.375/0.625=0.6 Lift 0.375/(0.625*0.625)=0.96 Leverage 0.375 - 0.390 = -0.015

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 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 class web and download run Magnum Opus demo

A store selling fruits and vegetables Which items are sold together frequently?

After you install the problem, you can see below initial screen 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 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 > … 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. Click GO 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

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