1. Pattern Lattice Traversal by Selective Jumps Osmar R. Zaïane and Mohammad El-Hajj Department of Computing Science, University of Alberta Edmonton, AB, Canada What is Leap traversal Approach A new approach that efficiently pinpoints maximal patterns at the border of the lattice of the frequent patterns by jumping in the lattice without applying the traditional depth or breadth traversal. Leap traversal approach consists of: 1. Finding the set of Frequent path bases; 2. Intersecting Frequent path bases to find candidate patterns and the support of the results; 3. Applying pruning theorems to the intersected set; 4. Generating either the set of maximal, closed or all. What is a frequent Path bases 1. At maximum one A-FPB can be generated from one transaction. 2. All frequent items in an A-frequent path base have support greater than or equal to the support of A; 3. Each A-FPB represents items that physically occur in the database with item A. 4. Each A-FPB has its branch-support, which represents the number of occurrences for this A-FPB in the database exactly alone (i.e. not as subset of other FPBs). In other words, the branch support of a pattern is the number of transactions that consist of this pattern, not the transactions that include this pattern along with other frequent items. The branch support is always less or equal to the support of a pattern.x 5. Each FPB is made of more than two itemsets How to find Frequent Path bases Can be generated by creating headerless Frequent Pattern tree. What is a header less Frequent Pattern tree? It is a the regular Frequent pattern tree (FP-tree) that has the followings properties: 1.No header table 2.Each node has two counters (support and participation) 3.A link list to connect all the leaf nodes of frequent path bases 13457891011 123459101112 1234578911 23678912 13456789 123456789 2610 6 11 Transactional databases Frequent Path bases Support of a pattern p = Branch Support SupersetFPBases where SupersetFPBases are Frequent pattern bases that are superset of P How to find a support of a pattern ? ItemsBranch Support A1345789 1 B123459 1 C123457891 D2367891 E134567891 F1234567891 Example Pruning Algorithms For all X, and Y in FPBs ordered lexicographically, if X∩Y is frequent then there is no need to intersect any other elements that have X ∩ Y., i.e, all children of X ∩ Y can be pruned For all X, Y, and W in FPBs ordered lexicographically, if X ∩ Y = X ∩ W and Y << W (i.e Y is left of Win the lexicographic tree) then there is no need to explore any children of X ∩ Y. For all X, Y,Z in FPBs ordered lexicographically, if X ∩Y is subset of X ∩Z then we can ignore the sub-tree X ∩Y ∩Z. For all X, Y,Z ∈ FPBs, if X ∩ Y is superset of X ∩ Z then we can ignore the sub-tree of X ∩ Z as long X ∩ Z is not Frequent 1 2 3 4 Tree of Frequent pattern intersections Tree of Frequent pattern of intersections After applying the Pruning Algorithms (C) A. Advantage of finding maximal first. B. Scalability with very large datasets. C. Memory usage. Experimental Results Conclusion We present a new way of traversing the pattern lattice to search for pattern candidates. The idea is to first discover maximal patterns and keep enough intermediary information to generate from these maximal patterns all types of patterns with their exact support based on the supports of other candidate patterns, namely the branch supports of the frequent pattern bases. 1 C∩D∩E (5) 3,7,8,9) A∩B (5) 1,3,4,5,9 A∩F (4) 1,3,4,5,7,8,9 B∩F (3) 1,2,3,4,5,9 C∩D (3) 2,3,7,8,9 C∩E (4) 1,3,4,5,7,8,9 C∩F (2) 1,2,3,4,5,7,8,9 D∩E (3) 3,6,7,8,9 D∩F(2) 2,3,6,7,8,9 F 1,2,3,4,5,6,8,9 NULL E 1,3,4,5,6,7,8,9 D 2,3,6,7,8,9 C 1,2,3,4,5, 7,8,9 B 1,2,3,4,5,9 A 1,3,4,5,7,8,9 E∩F(2) 1,3,4,5,6,7,8,9 1 4 1 2 33 2 333 A∩C (5) 3,7,8,9 Maximal Patterns are 1,3,4,5,9 3,7,8,9 2 6 Frequent 1 itemset 1 2 3 4 5 6 7 8 9 Support >= 5 Support = 5 3,7,8,9 is a subset of A,C,D,E,F Frequent Path Bases