1. Discovering Frequent Arrangements of Temporal Intervals Papapetrou, P. ; Kollios, G. ; Sclaroff, S. ; Gunopulos, D. ICDM 2005

2. Outlines 2  Introduction  Definition  The Arrangement Enumeration Tree  BFS-based Approach  DFS-based Approach  Hybrid DFS-based Approach  Experimental Evaluation  Conclusion

3. Introduction 3  In this paper the goal is to develop methods that discover temporal arrangements of correlated event intervals which occur frequently in a database.  BFS-based Approach  DFS-based Approach  Hybrid DFS-based Approach

4. Definition 4  Event Interval Temporal Relations

5. Cont. 5  event interval sequence or e-sequence : .  k-e-sequence  E.g.  5-e-sequence  {(A,1,7), (B,3,19), (D,4,30), (C,7,15), (C,23,42)}  an e-sequence database

6. Cont. 6  E.g.  This can be done by using the “AND” operand denoted by *.  (b) A|B * A|C * B>C  R = { |, ||, >, → } and *. A|B → CA|B>C

7. The Arrangement Enumeration Tree 7 N(1) N(2) N(k)

8. BFS-based Approach 8  The BFS-based approach uses an arrangement enumeration tree to discover the set of frequent arrangements.  Definition :  F k denote the complete set of frequent k -arrangements.  C k the set of candidate frequent k -arrangements.

9. 9  Scanning D and filtering with min_sup = 2.  /  F 1 = {{A}, {B}, {C}}

10. 10  Based on F 1 and the enumeration tree, N 2 is generated.  / N2N2

11. 11  For every pair of events in the arrangements, D is scanned to get all the types of relations between them, i.e. IM 2.  / IM 2

12. 12  If these relations satisfy the support threshold they are added to F 2.  F 2 :

13. 13  F 3 :  /  Output : F = A > B * A > C * B > C

14. DFS-based Approach 14  We must completely explore all the sub-arrangements on a path before moving to another one.  One more step is added to BFS-based Algorithm :  When a node is found to contain a frequent arrangement, each sub-arrangement is added to F and the corresponding expansions are made on the tree.  We can skip those expansions in the enumeration tree reducing the cost of computation.

15. Hybrid DFS-based Approach 15  We use a hybrid DFS approach that generates the first two levels of the tree using BFS and then follows DFS for the rest of the tree.  This would compensate for the multiple database scans.

16. Experimental Evaluation 16 medium densitysparse dense medium density

17. Conclusion 17  The BFS-based approach uses an arrangement enumeration tree to discover the set of frequent arrangements.  The DFS-based method further improves performance over BFS by reaching longer arrangements faster and hence eliminating the need for examining smaller subsets of these arrangements.