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 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 CaseAgeIncomeRiskCreditResult Red Green Green Amber Green Green Green Green Green Red1

Fuzzified Age Figure 2: The membership functions of attibute Age Age Membership value YoungMiddleOld

Fuzzify Age CaseAgeYoungMiddleOld

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 R 11 R R 22 R R 11 R R 22 R R 11 R R 31 R R 11 R R 31 R R 11 R R 31 R R 22 R R 41 R R 22 R R 42 R

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 R 22 R R 41 R R 41 R R 31 R R 22 R R 51 R R 51 R R 41 R R 31 R R 51 R

Rules vs. Support

Rules vs. Confidence

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