1. ICML-2002Xindong Wu, University of Vermont, USA 1 Mining both Positive and Negative Association Rules Xindong Wu (*), Chengqi Zhang (+), and Shichao Zhang (+) (*) University of Vermont, USA (+) University of Technology Sydney, Australia xwu@emba.uvm.edu

2. ICML-2002Xindong Wu, University of Vermont, USA 2 Outline Negative association rules: examples Frequent vs infrequent itemsets Defining negative association rules Procedure AllItemsOfInterest Extracting positive and negative rules Algorithm PositiveAndNegativeAssociations Some Experimental Results Related Work

3. ICML-2002Xindong Wu, University of Vermont, USA 3 Negative Association Rules E.g. 1: A =>B, E=>F, where to put C and D? (what if A =>~C) E.g. 2: t and c: frequent t U c: infrequent support(t U ~c) = support(t) – support(t U c) can be high How about t => ~c ?

4. ICML-2002Xindong Wu, University of Vermont, USA 4 Frequent vs Infrequent Itemsets A frequent itemset I: support(I) >= minsupp An infrequent itemset J: support(J) < minsupp How many possible itemsets (m baskets, n items)? 2 m (an expensive search process!)

5. ICML-2002Xindong Wu, University of Vermont, USA 5 Positive Association Rules (X=>Y) 1. X  Y =  2. Supp(X U Y)  minsupp 3. Conf(X U Y)  minconf 4. Supp(X U Y) / supp(X)  minconf

6. ICML-2002Xindong Wu, University of Vermont, USA 6 Negative Association Rules (1) If supp(A U B) < minsupp, A U B is infrequent If A is frequent, B is infrequent, A => ~B is a valid rule? Maybe, but not of our interest Heuristic Heuristic: Only if both A and B are frequent, will A => ~B be considered.

7. ICML-2002Xindong Wu, University of Vermont, USA 7 Negative Association Rules (2) 1. A  B =  2. Supp(A) >= minsupp, sub(B) > minsupp, and supp(A U ~B) >= minsupp 3. Supp(A U ~B) – supp(A)supp(~B) >= mininterest 4. Supp(A U ~B)/supp(A) >= minconf

8. ICML-2002Xindong Wu, University of Vermont, USA 8 Procedure AllItemsOfInterest Input: D (a database); minsupp; mininterest Output: PL (frequent itemsets); NL (infrequent itemsets) Design: Similar to Apriori, Frequent k is generated from Frequent k-1 See paper for details(?) See paper for details(?)

9. ICML-2002Xindong Wu, University of Vermont, USA 9 Extracting Positive and Negative Rules (1) supp(X U Y) p(Y|X) Interest(X,Y) = -------------------- = -------- supp(X)supp(Y) p(Y) If interest(X,Y) = 1, X and Y are independent. If interest(X,Y) > 1, Y is positively dependent on X. If interest(X,Y) < 1, Y is negatively dependent on X (~Y is positively dependent on X).

10. ICML-2002Xindong Wu, University of Vermont, USA 10 Extracting Both Types of Rules (2) p(Y|X)-p(Y) ---------------, if p(Y|X) >= p(Y), p(Y) <> 1 1 – p(Y) Confidence(X =>Y) = PR(Y|X) = p(Y|X)-p(Y) ---------------, if p(Y) > P(Y|X), p(Y) <> 0 p(Y)

11. ICML-2002Xindong Wu, University of Vermont, USA 11 3 Types of Negative Rules Definition 1 in the paper: A => ~B ~A => B ~A => ~B

12. ICML-2002Xindong Wu, University of Vermont, USA 12 Algorithm PositiveAndNegtative Associations Input: D – a database; minsupp, miniconf, mininterest Output: Association rules Algorithm PositiveAndNegativeAssociations (in the Paper) Design: Algorithm PositiveAndNegativeAssociations (in the Paper)

13. ICML-2002Xindong Wu, University of Vermont, USA 13 Experimental Results (1) A comparison with Apriori Table 2 in the paper.

14. ICML-2002Xindong Wu, University of Vermont, USA 14 Experimental Results (2) A comparison with no-pruning Table 3 in the paper

15. ICML-2002Xindong Wu, University of Vermont, USA 15 Related Work Negative relationships between frequent itemsets, but not how to find negative rules (Brin, Motwani and Silverstein 1997) Strong negative association mining using domain knowledge (Savasere, Ommiecinski and Navathe 1998)

16. ICML-2002Xindong Wu, University of Vermont, USA 16 Conclusions Negative rules are useful There could be more negative association rules if you have different conditions.