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Discovering Frequent Arrangements of Temporal Intervals

Discovering Frequent Arrangements of Temporal Intervals. Papapetrou , P . ; Kollios, G. ; Sclaroff, S. ; Gunopulos , D . ICDM 2005. Outlines. Introduction D efinition The Arrangement Enumeration Tree BFS-based Approach DFS-based Approach Hybrid DFS-based Approach

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Discovering Frequent Arrangements of Temporal Intervals

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

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

  3. Introduction • 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 • Event Interval Temporal Relations

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

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

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

  9. Scanning D and filtering withmin_sup= 2 . • / • F1= {{A}, {B}, {C}}

  10. Based on F1 and the enumeration tree, N2 is generated. • / N2

  11. For every pair of events in the arrangements, D is scanned to get all the types of relations between them, i.e. IM2. • / IM2

  12. If these relations satisfy the support threshold they are added to F2. • F2 :

  13. F3 : • / • Output : F = A > B * A > C * B > C

  14. DFS-based Approach • 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 • 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 medium density sparse sparse medium density dense dense

  17. Conclusion • 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.

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