1. Salvatore Ruggieri SIGKDD2010 Frequent Regular Itemset Mining 2010/9/2 1

2. Outline 2010/9/2 2 Motivation Problem Definition Mining Regular Itemsets Experimental Results Conclusions

3. Motivation 2010/9/2 3 The intended objective of concise representations, like as closed itemset, is to alleviate the problems due to extracting, storing and postprocessing a huge amount of frequent patterns. They sacrifice readability and direct interpretability by a data analyst in favor of a compact, lossless representation, where itemsets whose support is derivable from others are pruned away.

4. (Cont.) 2010/9/2 4 min_sup=2 15 frequent itemsets a: 3 b: 3 c: 3 d: 2 ab: 2 bc: 2 ac: 3 bd: 2 ad: 2 cd: 2 abc: 2 abd: 2 acd: 2 bcd: 2 abcd: 2 3 closed itemset

5. Problem Definition 2010/9/2 5 This paper propose an extension of itemsets, called regular, with an immediate semantics and interpretability.

6. Extended itemsets 2010/9/2 6 E::=a|a?| {a 1,…,a h } * | {a 1,…,a k } + a?: means an item a may or may not be present. {a 1,…,a h } * : means any subset of an itemset may be present. {a 1,…,a k } + : means any non-empty subset of an itemset may be present. Example: The extended itemset ab{cd} * is represented the set of itemsets {ab, abc, abd, abcd} The extended itemset ab?{cd} + is represented the set of itemsets {ac, ad, acd, abc, abd, abcd}

7. (Cont.) 2010/9/2 7 The semantics s e ( ) for extended items is defined as follows:

8. (Cont.) 2010/9/2 8 The notion of extended itemset does not take into account the cover nor the support of the itemsets in tis semantics. Example The extended itemset R =ab? Two itemsets belong to s(R), namely a and ab. However, ab a

9. Regular Itemsets 2010/9/2 9

10. Mining Regular Itemsets 2010/9/2 10 A non-compositional item is defined:

11. A Covering precedure 2010/9/2 11 Given a non-compositional itemset R’, computes a set R’’ of extended itemsets equivalent to R’ and pairwise disjoint.

12. 2010/9/2 12 R 1 = d{abcd} * d{abc} *

13. 2010/9/2 13 R 3 = bc{d} - {ba} - {ad} * = bc{d} - {a} - {ad} *

14. 2010/9/2 14 R=a{a} - b? S1 This means that no extended itemset is equivalent to R

15. 2010/9/2 15 R 2 = ba{d} - {cd} * =bac?

16. 2010/9/2 16 R = cd{ab} - {ab} * Partition the semantics s’(R) in two sets Removing any a? from R,

17. Merging Extended Itemsets 2010/9/2 17

18. 2010/9/2 18 Given the regular itemsets R 1 =bac? and R 2 =bc They can be merged to b{ac} +

19. 2010/9/2 19 Given the regular itemsets R 1 =b{ad} + and R 2 =bc{ad} * They can be merged to b{acd} +

20. Experimental Results 2010/9/2 20

21. Conclusion 2010/9/2 21 This paper introduced regular itemsets with an immediate semantics and interpretability.