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Association Rules
Olson
Yanhong Li
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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
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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
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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
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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
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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
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Demo Model: Loan AppCase Age Income Risk Credit Result
1 20 52623 -38954 Red 0
2 26 23047 -23636 Green 1
3 46 56810 45669 Green 1
4 31 38388 -7968 Amber 1
5 28 80019 -35125 Green 1
6 21 74561 -47592 Green 1
7 46 65341 58119 Green 1
8 25 46504 -30022 Green 1
9 38 65735 30571 Green 1
10 27 26047 -6 Red 1
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Fuzzified Age
Figure 2: The membership functions of attibute Age
0
0.2
0.4
0.6
0.8
1
1.2
0 25 35 40 50 100
Age
Mem
bersh
ip
value
Young Middle Old
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Fuzzify AgeCase Age Young Middle Old
1 20 1.000 0 0
2 26 0.9 0.1 0
3 46 0 0.4 0.6
4 31 0.4 0.6 0
5 28 0.7 0.3 0
6 21 1 0 0
7 46 0 0.4 0.6
8 25 1 0 0
9 38 0 1 0
10 27 0.8 0.2 0
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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
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Support
• If support for pair of categories is above minimum support, retain
• Identifies all pairs of fuzzy categories with sufficiently strong relationship
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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
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Confidence
• Identify direction
• For those training set cases involving the pair of attributes, what proportion came out as predicted?
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Confidence Values: PairsMinimum 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
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Rules vs. Support
Figure 7: The relationship between number of association rules and minsup using the proposed method
0
5
10
15
20
0.2 0.25 0.3 0.35 0.4 0.55minsup
minconf=0.55
minconf=0.65
minconf=0.75
minconf=0.85
minconf=0.95
minconf=1
the number of association rules
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Rules vs. Confidence
0
5
10
15
20
0.55 0.65 0.75 0.85 0.95 1
minconf
minsup=0.2
minsup=0.25
minsup=0.3
minsup=0.35
minsup=0.4
minsup=0.55
Figure 8: The relationship between number of association rules and
minconf using the proposed method
the number of
association rules
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Higher order combinations
• Try triplets– If ambitious, sets of 4, and beyond
• Problem:– Computational complexity explodes
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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