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Mining the Most Interesting Rules

Mining the Most Interesting Rules. Roberto J. Bayardo Jr., Rakesh Agrawal Presented by: Mohamed G. Elfeky. Introduction. Algorithms for mining rules: Constraint-based Heuristic (Predictive rules) Interestingness-metric Several interestingness metrics:

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Mining the Most Interesting Rules

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  1. Mining the Most Interesting Rules Roberto J. Bayardo Jr., Rakesh Agrawal Presented by: Mohamed G. Elfeky

  2. Introduction • Algorithms for mining rules: • Constraint-based • Heuristic (Predictive rules) • Interestingness-metric • Several interestingness metrics: • confidence, support, laplace, gain, conviction

  3. Generic Problem Statement The rule: A  C The input is: (U, D, , C, N) • U is a set of conditions for the rule antecedent. • D is a data-set. •  is a total order on rules. • C is a condition for the rule consequent. • N is a set of constraints on rules.

  4. Optimized Rule Mining • Find a set A1 U such that: • A1satisfiesN, •   A2  U: A2 satisfies N  A1 < A2. • Any rule A  C whose A  A1 is optimal. • Generally, this is NP-Hard problem.

  5. Partial-Order Optimized Rule Mining • Partial order vs. Total order • Some rules may be incomparable. • Several equivalence classes for optimal rules. • Find a set O P(U) such that: •  A O: A is optimal, • For each equivalence class that has a rule that is optimal, exactly one member of this class is within O.

  6. Monotonicity • f(x) is said to be monotone in x if: x1 < x2 f(x1)  f(x2) • f(x) is said to be anti-monotone in x if: x1 < x2 f(x1)  f(x2)

  7. Optimality • SC-Optimality • PC-Optimality • Definition • Theoretical Implications • Practical Implications

  8. SC-Optimality:Definition The partial order sc • For rules r1 and r2: r1 <scr2 if and only if: • sup(r1)  sup(r2)  conf(r1) < conf(r2), or • sup(r1) < sup(r2)  conf(r1)  conf(r2). • Also, r1 =scr2 if and only if: • sup(r1) = sup(r2)  conf(r1) = conf(r2).

  9. SC-Optimality:Definition (cont.) The partial order s c • For rules r1 and r2: r1 <s  cr2 if and only if: • sup(r1)  sup(r2)  conf(r1) > conf(r2), or • sup(r1) < sup(r2)  conf(r1)  conf(r2). • Also, r1 =s  cr2 if and only if: • sup(r1) = sup(r2)  conf(r1) = conf(r2).

  10. SC-Optimality:Definition (cont.) sc-optimal rule sc-optimal rule non-optimal rule confidence No optimal rules fall outside the borders support

  11. SC-Optimality:Theoretical Implications • A total order t is implied by scif: • r1 scr2  r1 tr2 ^ r1 =scr2  r1 =tr2 • r is optimal for scr is optimal for t. • t defined by f(r) is implied by scif: • f(r) is monotone in support, and • f(r) is monotone in confidence.

  12. SC-Optimality:Theoretical Implications (cont.) • Interestingness metrics: • laplace(r) = • gain(r) = sup(r) (1 – /conf(r)) • conviction(r) = /(1 – conf(r)) sup(r) + 1 sup(r)/conf(r) + k

  13. PC-Optimality:Definition The partial order pc • For rules r1 and r2: r1 <pcr2 if and only if: • pop(r1)  pop(r2)  conf(r1) < conf(r2), or • pop(r1)  pop(r2)  conf(r1)  conf(r2). • Also, r1 =pcr2 if and only if: • pop(r1) = pop(r2)  conf(r1) = conf(r2).

  14. PC-Optimality:Definition (cont.) • pop(A  C) is the set of records from D that satisfy both A and C. • |pop(r)| = sup(r)  |D| • Analogously, the definition of p  c

  15. PC-Optimality:Theoretical Implications • scis implied by pc and s  cby p  c. • pc results in more incomparable rule pairs. • pc-optimal rule set will contain more rules than sc-optimal rule set.

  16. Optimality:Practical Implications • Two algorithms are proposed, one for each type of optimality. • Each algorithm produces a set of optimal rules without specifying the interestingness metrics. • The produced set is guaranteed to identify the most interesting rules according to several metrics.

  17. Optimality:Practical Implications (cont.) • These algorithms facilitate interactivity: • Examine the optimal rules according to some metric without additional querying or mining. • Find the most interesting rule that characterizes any given subset of the population.

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