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Defining Negative Correlated Patterns (II)

  • Definition 2 (negative itemset-based)
    • X is a negative itemset if (1) X = Ā U B, where B is a set of positive items, and Ā is a set of negative items, |Ā|≥ 1, and (2) s(X) ≥ μ
    • Itemsets X is negatively correlated, if

\[ s(X)<\prod_{i=1}^{k} s(x_{i}), where, x_{i}\in X, s(x_{i})= support of x_{i} \]

  • This definition suffers a similar null-invariant problem
  • Definition 3 (Kulzynski measure-based) If itemsets X and Y are frequent, but (P(X|Y) + P(Y|X))/2 < є, where є is a negative pattern threshold, then X and Y are negatively correlated.
  • Ex. For the same needle package problem, when no matter there are 200 or 105 transactions, if є = 0.01, we have
      • (P(A|B) + P(B|A))/2 = (0.01 + 0.01)/2 < є

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