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Association Rules

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.

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Association Rules

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  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

  8. Membership value 1.2 1 0.8 0.6 0.4 0.2 0 Age 0 25 35 40 50 100 Young Middle Old Figure 2: The membership functions of attibute Age Fuzzified Age

  9. Fuzzify Age

  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

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

  14. Confidence Values: PairsMinimum confidence 0.9

  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

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