Association Rules
Olson
Yanhong Li
Fuzzy Association Rules
• Association rules mining provides
information to assess significant
correlations in large databases
• IF X THEN Y
• SUPPORT: degree to which relationship
appears in data
• CONFIDENCE: probability that if X, then Y
Association Rule Algorithms
• APriori
• Agrawal et al., 1993; Agrawal & Srikant, 1994
– Find correlations among transactions, binary
values
• Weighted association rules
• Cai et al., 1998; Lu et al. 2001
• Cardinal data
• Srikant & Agrawal, 1996
– Partitions attribute domain, combines
adjacent partitions until binary
Fuzzy Association Rules
• Most based on APriori algorithm
• Treat all attributes as uniform
• Can increase number of rules by
decreasing minimum support, decreasing
minimum confidence
– Generates many uninteresting rules
– Software takes a lot longer
Gyenesei (2000)
• Studied weighted quantitative association rules
in fuzzy domain
– With & without normalization
– NONNORMALIZED
• Used product operator to define combined weight and fuzzy
value
• If weight small, support level small, tends to have data
overflow
– NORMALIZED
• Used geometric mean of item weights as combined weight
• Support then very small
Algorithm
• Get membership functions, minimum
support, minimum confidence
• Assign weight to each fuzzy membership
for each attribute (categorical)
• Calculate support for each fuzzy region
• If support > minimum, OK
• If confidence > minimum, OK
• If both OK, generate rules
Demo Model: Loan App
Case
1
2
3
4
5
6
7
8
9
10
Age
20
26
46
31
28
21
46
25
38
27
Income
52623
23047
56810
38388
80019
74561
65341
46504
65735
26047
Risk
-38954
-23636
45669
-7968
-35125
-47592
58119
-30022
30571
-6
Credit Result
Red
0
Green
1
Green
1
Amber
1
Green
1
Green
1
Green
1
Green
1
Green
1
Red
1
Fuzzified Age
1.2
Membership
value
1
0.8
0.6
0.4
0.2
0
Age
0
25
35
Young
Figure 2: The membership functions of attibute Age
40
Middle
50
100
Old
Fuzzify Age
Case
1
2
3
4
5
6
7
8
9
10
Age
20
26
46
31
28
21
46
25
38
27
Young
1.000
0.9
0
0.4
0.7
1
0
1
0
0.8
Middle
0
0.1
0.4
0.6
0.3
0
0.4
0
1
0.2
Old
0
0
0.6
0
0
0
0.6
0
0
0
Calculate Support for Each Pair of
Fuzzy Categories
• Membership value
– Identify weights for each attribute
– Identify highest fuzzy membership category
for each case
• Membership value = minimum weight associated
with highest fuzzy membership category
• Support
– Average membership value for all cases
Support
• If support for pair of categories is above
minimum support, retain
• Identifies all pairs of fuzzy categories with
sufficiently strong relationship
Pairs: minsup 0.25
R11R22
0.235
R22R42
0.184
R11R31
0.207
R22R51
0.449
R11R41
0.212
R31R41
0.266
R11R42
0.131
R31R42
0.096
R11R51
0.230
R31R51
0.264
R22R31
0.237
R41R51
0.560
R22R41
0.419
R42R51
0.174
Confidence
• Identify direction
• For those training set cases involving the
pair of attributes, what proportion came
out as predicted?
Confidence Values: Pairs
Minimum confidence 0.9
R22R41
0.855
R41R31
0.462
R41R22
0.727
R31R51
0.825
R22R51
0.916
R51R31
0.410
R51R22
0.697
R41R51
0.972
R31R41
0.831
R51R41
0.870
Rules vs. Support
the number of
association
rules
20
minconf=0.55
minconf=0.65
minconf=0.75
minconf=0.85
15
minconf=0.95
10
minconf=1
5
0
0.2
0.25
0.3
0.35
0.4
minsup
0.55
Figure 7: The relationship between number of association rules and
minsup using the proposed method
Rules vs. Confidence
minsup=0.2
the number of
association rules
minsup=0.25
minsup=0.3
20
minsup=0.35
15
minsup=0.4
10
minsup=0.55
5
0
0.55
minconf
0.65
0.75
0.85
0.95
1
Figure 8: The relationship betw een number of association rules and
minconf using the proposed method
Higher order combinations
• Try triplets
– If ambitious, sets of 4, and beyond
• Problem:
– Computational complexity explodes
Research
• The higher the minimum support, the
fewer rules you get
• The higher the minimum confidence, the
fewer rules you get
• Weights can yield more rules
• Greatest accuracy seemed to be at
intermediate levels of support
– Higher levels of confidence