Association Rules

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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 gt minimum, OK
• If confidence gt minimum, OK
• If both OK, generate rules

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Demo Model Loan App
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Fuzzified Age

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Fuzzify Age
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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
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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
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Rules vs. Support
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Rules vs. Confidence
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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