Download Association Rules

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) AB
(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