1. 1 Summarizing Sequential Data with Closed Partial Orders Gemma Casas-Garriga Proceedings of the SIAM International Conference on Data Mining (SDM'05) Advisor ： Jia-Ling Koh Speaker ： Chun-Wei Hsieh 03/10/2006

2. 2 Introduction Closed patterns is a compact and significative set The number of closed patterns may be still quite large Summarizing closed patterns with post- processing

3. 3 Motivation, Which is better than the other ?

4. 4 Main steps Grouping Closed Sequential Patterns Obtaining Closed Partial Orders

5. 5 Grouping Closed Sequential Patterns A valid pair (S, T ) S ⊆ CS is a nonredundant set of closed sequences, whose tid lists are at least T T ⊆ D is the maximal set of transactions where all s ∈ S are contained.

6. 6 Grouping Closed Sequential Patterns

7. 7 A naive approach is to group closed sequences with the same tid list The naive way may miss some element Ex: ?

8. 8 Grouping Closed Sequential Patterns Let (S, T ) be a valid pair, then we have that S = t for all s ∈ S we have that tid(s) is at least T It has to use the transactions of the database

9. 9 Grouping Closed Sequential Patterns Given two valid pairs (S′, T′) and (S, T ), if T ⊆ T′ then for all s′ ∈ S′ there exists s ∈ S s.t. s′ ⊆ s. (S′, T ′ ) (S, T )

10. 10 Grouping Closed Sequential Patterns

11. 11 Grouping Closed Sequential Patterns

12. 12 Obtaining Closed Partial Orders obtain a compact representation from each valid pair (S, T ) A partial order can be modelled as a triple p = (V,E, l)

13. 13 Obtaining Closed Partial Orders Given a set of sequences S and let s, s′ ∈ S be two sequences s =, = if − = ; and, − head (s, I ) ⋄ tail (, j + 1) ⊆, for some ∈ S; and, − head (, j ) ⋄ tail ( s, i + 1) ⊆, for some ∈ S. then that position i of s matches with position j of ; note it by p[i] ∼ q[j].

14. 14 Obtaining Closed Partial Orders S={, } AC CCA C ACCA ACC CA CAC CA CCCA ACACCA CACCA ACCCA

15. 15 Obtaining Closed Partial Orders

16. 16 Obtaining Closed Partial Orders

17. 17 Obtaining Closed Partial Orders Using the transitivity property to improve the algorithm Transitivity: Given a valid pair (S, T ) let s,, ∈ S, if s[i] ∼ [j] and [j] ∼ [k], then s[i] ∼ [k].

18. 18 Simultaneity condition of input sequences

19. 19 Experiment 3 different sequential database Synthetic data (1000 transactions) The command history of a unix computer user (607 transactions) The first chapter of the book “ 1984 ” by George Orwell (340 transactions)

20. 20 Experiment

21. 21 Experiment

22. 22 Experiment