User-Defined%20Association%20Mining

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User-Defined Association Mining

• Ke Wang
• Simon Fraser University
• Yu He
• National University of Singapore

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Motivation

• Current one-framework-per-notion paradigm.
• The users may not find pre-determined framework
  suitable for their specific needs.

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Several examples

1. Causal relationships among multi-item events
   MALE?POSTGRAD ? HIGH_INCOME
2. HIGH_INCOME is more correlated with MALE?POSTGRAD
   than FEMALE?POSTGRAD
3. BEER is more correlated with CHIPS during
   6PM,9PM ?WEEKDAY than the general.

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Our approach

• User-Defined Association Mining (UDA mining).
• Define a language for specifying a broad class of
  associations and yet efficient to be implemented.
• Existing notions of association mining are
  instances of the UDA mining.
• Many new ad-hoc association mining tasks can be
  defined in the UDA mining framework.

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Definitions

• items and events
• A user-defined association is in the form of
• Z1,, Zp ? X1,, Xk
• subject events X1,, Xk
• context events Z1,, Zp
• Support_Filter P(X1Xk Zi) ? mini_sup
• Strength_Filter ?i ? mini_str i

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UDA specification

• UDA(z1,, zp ? x1,, xk) (kgt0, p ?0) has the
  form
• Strength_Filter(z1,, zp ? x1,, xk) ?
  Support_Filter(z1,, zp ? x1,, xk)
• symmetric vs asymmetric

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UDA problem

• Z1,, Zp ? X1,, Xk is a UDA if
• Xi ?Xj?, i?j, and
• Xi ?Zj?, i?j, and
• UDA(Z1,, Zp ? X1,, Xk) is true.
• The UDA problem to find all UDAs of the
  specified sizes 0ltk?k for a given UDA
  specification.

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Association rules

• Association rules Z? A introduced in AIS93 can
  be specified by
• Support_Filter(z ? x) P(zx) ? mini_sup
• Strength_Filter(z ? x) ?(z,x) ? mini_conf
• where ?(z,x) P(xz) is the confidence.

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Multiway correlation

• Events X1,, Xk are correlated when they occur
  together more often than expected when they are
  independent.
• ?(x1,, xk ) ?2(x1,, xk) ? ??2 BMS97, ? 5
• Uncorrelation 1/ ?2(x1,, xk) ? 1/ ??2, ? 95

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Conditional association

• Z ? X1,, Xk
• Strength_Filter(z ? x1,, xk)
• INTL ? BUSINESS_TRIP ? CEO, FIRST_CLASS

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Comparison association

• Z1, Z2 ? X
• Strength_Filter(z1, z2 ? x)
• Dist(?j(z1,x), ?j(z2,x)) ? mini_strj
• INTL ? BUSINESS_TRIP, PRIVATE_TRIP ? CEO ?
  FIRST_CLASS

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Emerging association

• Z1, Z2 ? X1,, Xk
• Strength_Filter(z1, z2 ? x1,, xk )
• Dist(?j(z1, x1,, xk ), ?j(z2, x1,, xk )) ?
  mini_strj

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Causal association

• CCC rule if events Z, X1, X2 are pairwise
  correlated, and if X1 and X2 are uncorrelated
  when conditioned on Z, one of the following
  causal relationships exists
• X1 ? Z ? X2, X1 ? Z ? X2 , X1 ? Z ? X2
• Strength_Filter(z ? x1 , x2)
• ?1(?, x1 , x2) ? mini_str1 ? ?1(?, x1 , z) ?
  mini_str1 ?
• ?1(?, x2 , z) ? mini_str1 ? ?2(z, x1 , x2) ?
  mini_str2

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The specification language

• ?j is a function of P(v) and v is a conjunction
  of any number of subject events Xi and zero or
  one context event Zj.
• Supports P(v) are available from mining large
  events because X1Xk Zi is large.
• Individual-context assumption(ICA)
• v satisfies the ICA if v is a conjunction of zero
  or more terms of the form Xi and ?Xi, and zero or
  one term of the form Zj and ?Zj.

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Implementation

• Step 1 find all large events by applying Apriori
  or its variants.
• Step 2 construct UDAs using large events.
• In k-th iteration, a k-tuple (X1,, Xk,Zi ) is
  generated from two (k-1)-tuple (X1,, Xk-1,Xk )
  and (X1,, Xk-1,Zi )
• After generating all k-tuples, we construct a
  candidate UDA Z1,, Zp ? X1,, Xk using p
  distinct tuples of the form (X1,, Xk,Zi ),
  i1,, p.

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Experiments

• census dataset 63 items, 126,229 transactions.
• Each transaction represents one individual.
• One item represents a boolean descriptor.

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Experiments
Some multiway correlations found
Some conditional associations found
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Experiments
Some comparison associations found
Some emerging associations found
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Experiments
Some CCC causal associations found