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 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

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

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

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: 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

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

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

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