Mining both Positive and Negative Association Rules

1. Mining both Positive and NegativeAssociation Rules Xindong Wu (*), Chengqi Zhang (+), and Shichao Zhang (+) (*) University of Vermont, USA (+) University of Technology Sydney, Australia xwu@emba.uvm.edu Xindong 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 Xindong 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 ? Xindong 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)? • 2m (an expensive search process!) Xindong Wu, University of Vermont, USA

5. Positive Association Rules (X=>Y) • XY =  • Supp(X U Y)  minsupp • Conf(X U Y)  minconf • Supp(X U Y) / supp(X)  minconf Xindong 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: Only if both A and B are frequent, will A => ~B be considered. Xindong Wu, University of Vermont, USA

7. Negative Association Rules (2) • A  B =  • Supp(A) >= minsupp, sub(B) > minsupp, and supp(A U ~B) >= minsupp • Supp(A U ~B) – supp(A)supp(~B) >= mininterest • Supp(A U ~B)/supp(A) >= minconf Xindong 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, Frequentk is generated from Frequent k-1 See paper for details(?) Xindong 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). Xindong 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) Xindong Wu, University of Vermont, USA

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

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

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

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

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