1. I. Association
Market Basket Analysis

2. 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%]

3. 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%]

4. 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

5. Rule Measures: Support and Confidence
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}
Customer
buys both
Customer
buys diaper
Customer
buys beer
Let minimum support 50%, and minimum confidence 50%, we have
A  C (50%, 66.6%)
C  A (50%, 100%)

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

7. 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

8. An Example of Market Basket(1(2)
Basic probabilities are below:
(1) AB
(2) (A, B)  C
Coverage
5/8 = 0.625
3/8 = 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 =
= 0.016

9. 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).

10. 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

11. 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)

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

13. 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).

14. 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

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

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

17. Click Yes and click Next > …

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

19. click Import Data를 클릭
Then, you can see a screen like below left.

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

21. 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 = : the support is (12.9 cases) greater than

22. 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

23. 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 =