1. Association Rules Olson Yanhong Li

2. 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

3. 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

4. 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

5. 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

6. 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

7. Demo Model: Loan App CaseAgeIncomeRiskCreditResult 12052623-38954Red0 22623047-23636Green1 3465681045669Green1 43138388-7968Amber1 52880019-35125Green1 62174561-47592Green1 7466534158119Green1 82546504-30022Green1 9386573530571Green1 102726047-6Red1

8. Fuzzified Age Figure 2: The membership functions of attibute Age 0 0.2 0.4 0.6 0.8 1 1.2 025354050100 Age Membership value YoungMiddleOld

9. Fuzzify Age CaseAgeYoungMiddleOld 1201.00000 2260.90.10 34600.40.6 4310.40.60 5280.70.30 621100 74600.40.6 825100 938010 10270.80.20

10. 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

11. Support If support for pair of categories is above minimum support, retain Identifies all pairs of fuzzy categories with sufficiently strong relationship

12. Pairs: minsup 0.25 R 11 R 22 0.235R 22 R 42 0.184 R 11 R 31 0.207R 22 R 51 0.449 R 11 R 41 0.212R 31 R 41 0.266 R 11 R 42 0.131R 31 R 42 0.096 R 11 R 51 0.230R 31 R 51 0.264 R 22 R 31 0.237R 41 R 51 0.560 R 22 R 41 0.419R 42 R 51 0.174

13. Confidence Identify direction For those training set cases involving the pair of attributes, what proportion came out as predicted?

14. Confidence Values: Pairs Minimum confidence 0.9 R 22 R 41 0.855R 41 R 31 0.462 R 41 R 22 0.727R 31 R 51 0.825 R 22 R 51 0.916R 51 R 31 0.410 R 51 R 22 0.697R 41 R 51 0.972 R 31 R 41 0.831R 51 R 41 0.870

15. Rules vs. Support

16. Rules vs. Confidence

17. Higher order combinations Try triplets –If ambitious, sets of 4, and beyond Problem: –Computational complexity explodes

18. 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