Discovering Frequent Arrangements of Temporal Intervals Papapetrou, P. ; Kollios, G. ; Sclaroff, S. ; Gunopulos, D. ICDM 2005
Outlines 2 Introduction Definition The Arrangement Enumeration Tree BFS-based Approach DFS-based Approach Hybrid DFS-based Approach Experimental Evaluation Conclusion
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
Definition 4 Event Interval Temporal Relations
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
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
The Arrangement Enumeration Tree 7 N(1) N(2) N(k)
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 Scanning D and filtering with min_sup = 2. / F 1 = {{A}, {B}, {C}}
10 Based on F 1 and the enumeration tree, N 2 is generated. / N2N2
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 If these relations satisfy the support threshold they are added to F 2. F 2 :
13 F 3 : / Output : F = A > B * A > C * B > C
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.
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.
Experimental Evaluation 16 medium densitysparse dense medium density
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.