Association Rules

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Association Rules

• Hawaii International Conference on System
  Sciences (HICSS-40)
• January 2007
• David L. 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
• Initial data mining analysis
• Not predictive
• 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 Analysis

• Deal with vagueness uncertainty
• Fuzzy Set Theory
• Zadeh 1965
• Probability Theory
• Pearl 1988
• Rough Set Theory
• Pawlak 1982
• Set Pair Theory
• Zhao 2000

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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 by Single Item
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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
• For outcomes, R51 (On Time) strong,
• R52 (Default) not

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Support by Pair minsup 0.25
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Support by Triplet minsup 0.25
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Quartets

• None qualify, so algorithm stops

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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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4 Rules

• IF Income is Middle THEN Outcome is On-Time
• R22?R51 support 0.490 confidence 0.916
• IF Credit is Good THEN Outcome is On-Time
• R41?R51 support 0.576 confidence 0.972
• IF Income is Middle AND Credit is Good THEN
  Outcome is On-Time
• R22R41?R51 support 0.419 confidence 0.995
• IF Risk is High AND Credit is Good THEN Outcome
  is On-Time
• R31R41?R51 support 0.266 confidence 0.993

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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
• Here, none
• Problems
• Computational complexity explodes
• Doesnt guarantee total coverage
• That also would explode complexity
• Can control by lowering minsup, minconf

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Simulation Testing

• Selected 550 cases
• Held out 100
• Randomly assigned weights to each fuzzy region of
  each attribute
• minsup 0.35, 0.45, 0.55, 0.65
• minconf 0.7, 0.8, 0.9

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Simulation Results