The Challenge of Mining Billions of Transactions

Transcription

1 Faculty of omputer Science The hallenge of Mining illions of Transactions Osmar R. Zaïane International Workshop on lgorithms for Large-Scale Information Processing in Knowledge iscovery Laboratory ata Mining Research Group 008 Size of real data Wal-Mart registers 00 million transactions a week March 00 VIS processes 0 million events a day ecember 007 Yahoo! has 00 million users per month February 008 Why research papers only talk about datasets with about few hundred thousand transactions? Is this realistic scalability? What are the challenges for real large-scale data? in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

2 Roadmap Introduction What are frequent patterns and why are they important? Why is it difficult, it s simple counting after all? Mining xtremely Large atasets: the hallenges Subsets of patterns onstraint pushing Parallelization The Leap and ifold-leap pproaches Improving upon Leap in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Why Studying Frequent Pattern Mining? Frequent pattern mining Foundation for several essential data mining tasks: ssociation rule mining Sequential pattern mining ontrast set mining ssociative classifiers lustering nalysis pplications: basket data analysis, cross-marketing, catalog design, loss-leader analysis, clustering, classification, Web log sequence, N analysis, etc. in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

3 Frequent Itemset Generation null With items we have are = possible candidate itemsets Given d items, there are d possible candidate itemsets in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 priori lgorithm Idea Level-wise algorithm. Generate candidate itemsets of a particular size. Scan the database to see which of them are frequent n itemset is frequent if all its subsets are frequent. Use only these frequent itemsets to generate the set of candidates with size=size+ R. grawal & R. Srikant, VL 99 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

4 FP-Growth Grow long patterns from short ones using local frequent items abc is a frequent pattern Get all transactions having abc : abc d is a local frequent item in abc abcd is a frequent pattern J. Han, J. Pei, Y. Yin, SIGMO 00 laims to be order of magnitude faster than priori FP-Tree Patterns Recursive conditional trees and FP-Trees in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Illustrating priori Principle Infrequent Items Pruned supersets in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

5 Mining xtremely Large atabases Issues and suggestions? Mining for Frequent patterns is an active research area since the last two decades. Many efficient algorithms exists. Many conferences, and workshops are conducted. So, what is still missing? Mining xtremely large databases is still a problematic issue urrent databases could have hundreds of millions if not billions of transactions Unfortunately we cannot [easily] mine them for frequent patterns in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Mining xtremely Large atabases Issues and suggestions? What to do? ) Investigate finding special patterns (Subsets of the LL patterns) losed patterns Maximal patterns ) Pushing constraints during the mining process ) Parallel implementations of existing sequential algorithms in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

6 Other Frequent Patterns Frequent pattern {a,, a 00 } ( 00 ) + ( 00 ) + + ( ) = 00 - =.7*0 0 frequent sub-patterns! Frequent losed Patterns Frequent Maximal Patterns ll Frequent Patterns ll frequent itemsets losed frequent itemsets Maximal frequent itemsets Maximal frequent itemsets losed frequent itemsets ll frequent itemset in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Frequent losed Patterns For frequent itemset X, if there exists no item y such that every transaction containing X also contains y, then X is a frequent closed pattern In other words, frequent itemset X is closed if there is no item y, not already in X, that always accompanies X in all transactions where X occurs. oncise representation of frequent patterns. an generate all frequent patterns with their support from frequent closed ones. Reduce number of patterns and rules N. Pasquier et al. In IT 99 in Knowledge iscovery PK 008 {abcd} {abc} {bd} Transactions Support = a b c d ab ac bc bd abc Frequent itemsets b bd abc Frequent losed itemsets Osaka, Japan May 0, 008 O.R. Zaïane 008

7 Frequent Maximal Patterns Frequent itemset X is maximal if there is no other frequent itemset Y that is superset of X. In other words, there is no other frequent pattern that would include a maximal pattern. More concise representation of frequent patterns but the information about supports is lost. an generate all frequent patterns from frequent maximal ones but without their respective support. R. ayardo. In SIGMO 98 in Knowledge iscovery PK 008 {abcd} {abc} {bd} Transactions Support = a b c d ab ac bc bd abc Frequent itemsets bd abc Frequent Maximal itemsets Osaka, Japan May 0, 008 O.R. Zaïane 008 TI Items Maximal vs. losed Itemsets null Transaction Ids Not supported by any transactions in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

8 Maximal vs. losed Itemsets null losed but not maximal losed and maximal Frequent Pattern order Minimum support = in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 onstraint-based frequent patterns Finding all the patterns in a database autonomously? unrealistic! The patterns could be too many but not focused! ata mining should be an interactive process User directs what to be mined using a data mining query language (or a graphical user interface) onstraint-based mining User flexibility: provides constraints on what to be mined System optimization: explores such constraints for efficient mining constraint-based mining in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

9 nti-monotonicity in onstraint-ased Mining nti-monotonicity When an intemset S violates the constraint, so does any of its superset sum(s.price) v is anti-monotone sum(s.price) v is not anti-monotone xample. : range(s.profit) is antimonotone Itemset ab violates So does every superset of ab TI T (min_sup=) Item a b c d e f Transaction a, b, c, d, f b, c, d, f, g, h a, c, d, e, f c, e, f, g Profit g h 0-0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Monotonicity in onstraint-ased Mining T (min_sup=) Monotonicity When an intemset S satisfies the constraint, so does any of its superset sum(s.price) v is monotone TI Transaction a, b, c, d, f b, c, d, f, g, h a, c, d, e, f c, e, f, g Item Profit min(s.price) v is monotone xample. : range(s.profit) Itemset ab satisfies So does every superset of ab a b c d e f g h in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

10 The onstraints FIM lgorithms (State of the rt) FI M J. Pie and J. Han. SIGK 000 ual Miner. ucil, J. Gherke,. Kiefer and W. White, SIGK 0 xaminer F. onchi, F. Giannotti,. Mazzanti, and. Pedreschi. IM 00 FP-onsai F. onchi and. Goethals. PK 00 ifoldleap M. l-hajj, P. Nalos and O. Zaiane, IM 0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Parallel Frequent itemset RPLIT candidate sets lgorithms andidate Set andidate Set andidate Set Replication lgorithms Partitioning lgorithms Hybrid lgorithms Replicate andidate Sets Partition the databases Partitioned database ount istribution algorithm (grawal R. et al, 99) Parallel Partition algorithm (shok Savasere et al, 99) Fast istributed algorithm (avid heung et al, 99) Parallel ata Mining algorithm (J.S. Park et al, 99) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

11 Parallel Frequent itemset lgorithms P. andidate Set andidate sets Partitioned P. andidate Set P. andidate Set Replication lgorithms Partitioning lgorithms Hybrid lgorithms -Partition the andidate Set -Need to Scan the whole data database ata istribution algorithm (grawal R. et al, 99) Intelligent ata istribution algorithm (-H Han et all, 997) Non Partitioned apriori, Simple partitioned, Hash Partitioned apriori and HP_L algorithms (Takahiko et al, 99) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Parallel Frequent itemset lgorithms P. andidate Set andidate sets Partitioned P. andidate Set P. andidate Set Replication lgorithms Partitioning lgorithms Hybrid lgorithms -ombine both ideas of replication and partition Partitioned database Hybrid istribution algorithm (-H Han et all, 997) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

12 How to mine extremely large databases? What can help us in mining large databases ) Investigate finding special patterns losed patterns Maximal patterns ) Pushing constraints ) Parallel implementations of existing sequential algorithms Still Mining extremely large databases is not feasible in practice in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 So, Where is the problem? Open Problems exists such as: How to mine extremely large databases? What can help us in mining large databases ) Investigate finding special patterns losed patterns Maximal patterns ) Pushing constraints ) Parallel implementations of existing sequential algorithms.observations on Superfluous Processing.Superfluous Search of the Lattice.Huge Memory structures used.parallel implementations are mainly priori based and parallelization of existing algorithms in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

13 Transaction Layout Horizontal Layout ach transaction is recorded as a list of items Transaction I Items G H M F N N O P Q R G 7 H I G 8 L F K 9 F M N O 0 F P J R H I K L M G O F P Q J F I J 7 K F 8 L andidacy generation can be removed [or reduced] (FP-Growth) Superfluous Processing in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Transaction Layout Vertical Layout Tid-list is kept for each item Transaction I Items G H M F N N O P Q R G 7 H I G 8 L F K 9 F M N O 0 F P J R H I K L M G O F P Q J F I J 7 K F 8 L Items Transaction I F G 7 H 7 I 7 J 0 K 8 7 L 8 8 M 9 N 9 O 9 P 9 Q R 0 Minimize Superfluous Processing andidacy generation is required in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

14 Transaction Layout itmap Layout Matrix : Rows represent transactions olumns represent item If item exists in transaction then cell value = else cell value = 0 T# Items T G T H T M T F N T N O P T Q R G T7 H I G T8 L F K T9 F M N O T0 F P J R T H I T K L T M G O T F P Q J T F I T J T7 K F T8 L Transaction I items T# F G H I J K L M N O P Q R T T T T T T T T T T T T T T T T T T Similar to horizontal layout. Suitable for datasets with small dimensionality in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Inverted Matrix Layout Interactive mining hanging the support level means expensive steps (whole process is redone) valuation and Presentation Knowledge Selection and Transformation ata warehouse ata Mining Patterns atabases in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

15 Why the Matrix Layout Repetitive tasks, (I/O) readings (Superfluous Processing) T# Items T# Items T G T G T H T G T M T G T F N T F G Support > T N O P T G G G T Q R G T G G G T7 H I G T7 G G G T8 L F K Frequent -itemsets {,,,,, F} T8 G F G T9 F M N O Non frequent items {G, H, I, J, K, L, M, N, O, P, Q, R} T9 F G G G T0 F P J R T0 F G G G T H I T G G T K L T M G O T F P Q J T G G T G G G T F G G G T F I T F G T J T G T7 K F T7 G F T8 L T8 G in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Why the Matrix Layout Repetitive tasks, (I/O) readings (Superfluous Processing) T# T Items G T H T M T F N T N O P T Q R G T7 H I G T8 L F K T9 F M N O T0 F P J R T H I T K L T M G O T F P Q J T F I T J T7 K F T8 L Support > 9 Frequent -itemsets {,, } Non frequent items {,, F, G, H, I, J, K, L, M, N, O, P, Q, R} T# T Items G G T G G G T G G G T G G G T G G G T G G G T7 G G G T8 G G G G T9 G G G G T0 G G G G T G G G T G G G G T G G G G T G G G G T G G G G T G G G T7 G G G T8 G G in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

16 Why the Matrix Layout Loc Index R Q P O N M 7 L 8 K 9 J 0 I H G F Transactional rray Transaction I Items G H M F N N O P Q R G 7 H I G 8 L F K 9 F M N O 0 F P J R H I K L M G O F P Q J F I J 7 K F 8 L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Why the Matrix Layout <G,,,,> Loc Index R Q P O N M 7 L 8 K 9 J 0 I H G F Transactional rray T# Items T G T H T M T F N T N O P T Q R G T7 H I G T8 L F K T9 F M N O T0 F P J R T H I T K L T M G O T F P Q J T F I T J T7 K F T8 L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

17 Why the Matrix Layout <G,,,,> <H,,,,> Loc Index Transactional rray R Q P O N M 7 L 8 K 9 J 0 I H (,) G (,) F 7 8 (,) 9 (,) (,) 0 (7,) (7,) 7 0 (8,) (, ) 8 (, ) T# Items T G T H T M T F N T N O P T Q R G T7 H I G T8 L F K T9 F M N O T0 F P J R T H I T K L T M G O T F P Q J T F I T J T7 K F T8 L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Why the Matrix Layout Loc Index Transactional rray R (,) (,) Q (,) (,) P (,) (9,) (9,) O (,) (,) (,) N (,) (7,) (,) M (,) (,) (,) 7 L (8,) (8,) (,9) 8 K (,) (,) (,7) 9 J (,) (,) (,7) 0 I (,) (,) (,) H (,) (,),) G (,) (,) (,) (,) F 7 (,) (,) (8,7) (,) (,8) (,) (,8) 8 (,) (,) (,) (7,) (,) (,7) (,8) (,9) 9 (,) (,) (7,) (7,) (7,7) (,7) (7,8) (7,9) (,0) 0 (7,) (7,) (8,) (8,) (8,) (, ) (, ) (, ) (8,0) (7,0) 7 0 (8,) (, ) (8,) (8,) (, ) (8,8) (, ) (, ) (8,9) (8,) 8 (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

18 Why the Matrix Layout Inverted Matrix Layout Support > Loc Index Transactional rray R (,) (,) Q (,) (,) P (,) (9,) (9,) O (,) (,) (,) N (,) (7,) (,) M (,) (,) (,) 7 L (8,) (8,) (,9) 8 K (,) (,) (,7) 9 J (,) (,) (,7) 0 I (,) (,) (,) H (,) (,),) G (,) (,) (,) (,) F 7 (,) (,) (8,7) (,) (,8) (,) (,8) 8 (,) (,) (,) (7,) (,) (,7) (,8) (,9) 9 (,) (,) (7,) (7,) (7,7) (,7) (7,8) (7,9) (,0) 0 (7,) (7,) (8,) (8,) (8,) (, ) (, ) (, ) (8,0) (7,0) 7 0 (8,) (, ) (8,) (8,) (, ) (8,8) (, ) (, ) (8,9) (8,) 8 (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) order Support in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Why the Matrix Layout Loc Index Transactional rray F 7 (,) (,) (8,7) (,) (,8) (,) (,8) 8 (,) (,) (,) (7,) (,) (,7) (,8) (,9) 9 (,) (,) (7,) (7,) (7,7) (,7) (7,8) (7,9) (,0) 0 (7,) (7,) (8,) (8,) (8,) (, ) (, ) (, ) (8,0) (7,0) 7 0 (8,) (, ) (8,) (8,) (, ) (8,8) (, ) (, ) (8,9) (8,) 8 (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

19 Why the Matrix Layout Loc Index Transactional rray F 7 (,) (,) (8,7) (,) (,8) (,) (,8) 8 (,) (,) (,) (7,) (,) (,7) (,8) (,9) 9 (,) (,) (7,) (7,) (7,7) (,7) (7,8) (7,9) (,0) 0 (7,) (7,) (8,) (8,) (8,) (, ) (, ) (, ) (8,0) (7,0) 7 0 (8,) (, ) (8,) (8,) (, ) (8,8) (, ) (, ) (8,9) (8,) 8 (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) T# T Items T T T F T T T7 T8 F T9 F T0 F T T T T F T F T T7 F T8 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Mining the Pattern Lattice (Traversal pproaches) ottom-up It uses current items at level k to generate items of level k+ (many database scans) Top-own It uses current items at level k+ to generate items of level k (favored when mining long frequent patterns) Hybrid null readth epth Hybrid approach It mines using both direction at the same time in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

20 Leap Traversal xample null Steps ottom x TI Items x Itemset is candidate if it is marked or if it is a subset of more than one infrequent marked superset How to find the x x Support of an itemset. Full scan of the database OR. Intelligent techniques: Support of itemset = Top Summation of the supports of its supersets of marked patterns Frequent Path bases in Knowledge iscovery PK candidates to check frequent patterns without checking Osaka, Japan May 0, 008 O.R. Zaïane 008 How can we generate Frequent Path ases? OFI trees Header less Frequent Pattern tree in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

21 OFI algorithm big picture OFI I/O scans reduced candidacy generation Small memory footprint FP-Tree OFI- trees Patterns in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Transactional database mined with support >= in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

22 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Find Frequent Items in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Remove none frequent items in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

23 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Sort Frequent items in escending order based on their support in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 How to Find Frequent Path ases? Headless Frequent Pattern tree example:,,0 NULL,,0,,0,,0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

24 How to Find Frequent Path ases? Headless Frequent Pattern tree example:,,0 NULL,,0,,0,,0,,0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 How to Find Frequent Path ases? Headless Frequent Pattern tree example:,,0 NULL,,0,,0,,0,,0,,0,,0,,0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

25 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Scan From Leaf to root to generate FP NULL Support ranch = Support ranch support,7,0,9,0,,0 Support Participation,,0,,0,,0,,0,,0,,0,,0,,0,,0 in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 How to Find Frequent Path ases? Headless Frequent Pattern tree example: Occurs times in Occurs time in Frequency counting What is the support of,, Occurs times in Total Support = Frequent Path ases Support ranch in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

26 How to find the maximal patterns? y all applying all possible intersection among the FP (asic pproach) NUL L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () Pruning Strategies For all X, and Y in FPs ordered lexicographically, if X Y is frequent then there is no need to intersect any other elements that have X Y NUL., i.e, all children of X Y can be pruned L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

27 Pruning strategies () Pruning Strategies For all X, and Y in FPs ordered lexicographically, if X Y is frequent then there is no need to intersect any other elements that have X Y NUL., i.e, all children of X Y can be pruned L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () Pruning Strategies For all X, and Y in FPs ordered lexicographically, if X Y is frequent then there is no need to intersect any other elements that have X Y NUL., i.e, all children of X Y can be pruned L in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

28 Pruning strategies () For all X, Y, and W in FPs 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. Pruning Strategies NUL L ssume = in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () For all X, Y, and W in FPs 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. Pruning Strategies NUL L ssume = p in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

29 Pruning strategies () For all X, Y, and W in FPs 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. Pruning Strategies NUL L ssume = in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () For all X, Y,Z in FPs ordered lexicographically, if X Y is subset of X Z then we can ignore the sub-tree X Y Z. Pruning Strategies NUL L ssume is subset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

30 Pruning strategies () For all X, Y,Z in FPs ordered lexicographically, if X Y is subset of X Z then we can ignore the sub-tree X Y Z. Pruning Strategies NUL L ssume is subset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () For all X, Y,Z in FPs ordered lexicographically, if X Y is subset of X Z then we can ignore the sub-tree X Y Z. Pruning Strategies NUL L ssume is subset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

31 Pruning strategies () For all X, Y,Z in FPs, 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 Pruning Strategies NUL L ssume is a superset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () For all X, Y,Z in FPs, 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 Pruning Strategies NUL L ssume is a superset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

32 Pruning strategies () For all X, Y,Z in FPs, 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 Pruning Strategies NUL L ssume is a superset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Pruning strategies () For all X, Y,Z in FPs, 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 Pruning Strategies NUL L ssume is a superset of in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

33 The Set of Maximal Patterns t this stage we have the set of Maximal Patterns with the set of Frequent Path ases. We can generate all subsets of this maximals with their support using the FP branch supports In our implementation we used bitmaps for itemset presentations: N Operation is used for the intersections and for subset checking Using The set of Maximal Patterns with the FP we can generate the set of LL or LOS Patterns lgorithms are either called OFI-Leap or HFP-Leap in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 xperiments (Samples on real data) High Support Low Support in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

34 Mining relatively small synthetic datasets mining for LL patterns in small synthetic dataset mining for LOS patterns in small synthetic dataset Time in seconds OFI-LL FP-Growth MFI Time in seconds OFI-LOS FPLOS MFI K 0K 00K 0K 0 0K 0K 00K 0K transaction size transaction size mining for MXIML patterns in synthetic dataset Time in seconds OFI-MX FPMX MFI 0 0K 0K 00K 0K transaction size in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 xperiments (Memory Usage) Support = %, % of Memory usage. HFP-Leap MFI % OFI-Leap % % FPMX 8% GNMX 7% OFI-Leap HFP-Leap GNMX FPMX MFI Support = %, % of Memory usage. Mining Retail ataset OFI-Leap MFI % % FPMX 8% GNMX 7% HFP-Leap % OFI-Leap HFP-Leap GNMX FPMX MFI in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

35 xperiments (xtremely Large datasets) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Leap with onstraints (ifoldleap) Push both types of constraints (Monotone and nti-monotone) in duality. uring the mining process Two Strategies are being adopted:. Push onstraints to prune. void onstraints checking in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

36 ifold Leap (Leap with constraints) F F F F F G H I J K L J K L F G H I Intersecting FP Frequent-Path-ases F F,,,, F F F F F F F F F F F F F F F F F F F F F F F F F F F F F Head (H): Is a frequent path base or any subset generated from the intersection of frequent path bases Tail (T): Is the itemset generated from intersecting all remaining frequent path bases not used in the intersection of (H) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 ifold Leap (Leap with constraints) Theorem : If an intersection of frequent path bases (H) fails Q(), it can be discarded, and there is no need to evaluate further intersections with (H). F Fails Q() Monotone onstraints F F F F F F ll subsets will also fails Q() F F F F F F F F F F F F F TOP OWN TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

37 ifold Leap (Leap with constraints) Theorem : If an intersection of frequent path bases (H) fails Q(), it can be discarded, and there is no need to evaluate further intersections with (H). F F F F F Fails Q() ll subsets will also fails Q() Prune H() with all its subsets F F F TOP OWN TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 ifold Leap (Leap with constraints) Theorem : If an intersection of frequent path bases (H) passes P(), it is a candidate P-maximal, and there is no need to evaluate further intersections with (H). F Passes P() nti-monotone onstraints F F F F F F ll subsets will also Pass P() F F F F F F F F F F F F F TOP OWN TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

38 ifold Leap (Leap with constraints) Theorem : If an intersection of frequent path bases (H) passes P(), it is a candidate P-maximal, and there is no need to evaluate further intersections with (H). F F F F F F F F F F F F F F F F Passes P() ll subsets will also Pass P() No need to test against P() for all subsets of (H) F F F F Reduce evaluations numbers TOP OWN TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 ifold Leap (Leap with constraints) Theorem : If a node s (H) (T) fails P(), the (H) node can be discarded, and there is no need to evaluate further intersections with (H). F F F F F Fails P() ll Superset will also fails P() F F F OTTOM UP TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

39 ifold Leap (Leap with constraints) Theorem : If a node s (H) (T) fails P(), the (H) node can be discarded, and there is no need to evaluate further intersections with (H). Fails P() ll Superset will also fails P() Prune H() with all its subsets OTTOM UP TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 ifold Leap (Leap with constraints) Theomrem :If a node s (H) (T) passes Q(), Q() is guaranteed to pass for any itemset resulting from the intersection of a subset of the frequent path bases used to generate (H) plus the remaining frequent path bases yet to be intersected with (H). Q() does not need to be checked in these cases. F F F F F Pass Q() ll Superset will also pass Q() F F F OTTOM UP TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

40 ifold Leap (Leap with constraints) Theomrem :If a node s (H) (T) passes Q(), Q() is guaranteed to pass for any itemset resulting from the intersection of a subset of the frequent path bases used to generate (H) plus the remaining frequent path bases yet to be intersected with (H). Q() does not need to be checked in these cases. F F F F F F F F Pass Q() ll Superset will also fails Q() No need to test against Q() for all supersets of (H) Reduce evaluations numbers OTTOM UP TSTING in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 i-irectional Pushing of constraints Theorems applied at the (H) F F F F F F F F F F F F F F F F Theorem : To prune subsets Theorem : To reduce constraints evaluations Theorems applied at the (H T) Theorem : To prune supersets Theorem : To reduce constraints evaluations F F F F in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

41 Results of ifold Leap Set of maximal patterns that satisfies both P() and Q() (P-Maximal) ll subsets of these patterns are guaranteed to satisfy P() The subsets are only testes against Q() The final sets are the set of frequent patterns that satisfies both P() and Q() in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Performance valuation ifoldleap (Q only) ualminer (Q only) ifoldleap (P only) ualminer (P only) ifoldleap (P & Q) ualminer (P & Q) retail dataset 00 Pushing P(), Q() and P() N Q() on the retail datasets Time in seconds Support 0.7% 0.% 0.08% ifoldleap (Q only) ualminer (Q only) ifoldleap (P only) ualminer (P only) ifoldleap (P & Q) ualminer (P & Q) retail dataset Time in seconds Support 0.7% 0.% 0.08% in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

42 Performance valuation Scalability tests ifoldleap (P & Q) ualminer (P & Q) Time in seconds transaction size 0K 00K 0K 00K in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Parallel Leap in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

43 Parallel Leap xample: Processors. in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Parallel Leap xample: Processors. Trees istributions. irect. Round Robin. First Last in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

44 Parallel ifold-leap xample: in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Parallel ifold-leap xample: Trees istributions. irect. Round Robin. First Last in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

45 Parallel xperiments Our experiments are conducted using a cluster made of boxes ach box has a linux..8 dual processor.ghz M,. G RM. Nodes are connected using Fast ethernet and Myrinet 000 network in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 xperiments Test Scalability: ifferent transactions sizes (p=) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

46 xperiments Test Scalability: ifferent number of processors (TS = 00Millions) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 xperiments Test Speedup: ifferent support values (TS = 00Millions) in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

47 xperiments ffect of Leap node distribution in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 onclusion and Future work framework of sequential and parallel algorithms can be implemented to mine extremely large databases by applying two strategies which are: y using a novel traversal searching for frequent patterns while using minimal memory requirements. y designing algorithms specially made for parallel execution rather than parallelizing an algorithm designed for a sequential execution. in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

48 onclusion and Future work Open Questions are still exist in this research area What algorithm is considered the best? How to determine database characteristics? What patterns to generate? in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Heterogeneous omputer lusters omputer clusters evolve in time by addition and suppression of nodes lusters are bound to become heterogeneous omputer clusters are now distributed geographically (grids) How to manage parallel mining and dynamic load balancing on heterogeneous clusters? How to manage parallel mining when the pipeline becomes the bottleneck and is inconsistent. in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008

49 symmetric Parallel ata Mining Frequent itemset mining: Many algorithms exist No real winner epends on dataset What determines the best algorithm to use given a dataset? partition a b c d n Scenario ll nodes use the same algorithm Scenario Nodes use different algorithms etermine new data partitioning strategies. reate new communication protocols. evise new load balancing techniques. Invent new parallel algorithms. in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008 Thank you UNIVRSITY OF LRT Osmar R. Zaïane, Ph.. ssociate Professor thabasca Hall dmonton, lberta anada TG 8 Telephone: Office + (780) 9 80 Fax + (780) mail: zaiane@cs.ualberta.ca Questions? in Knowledge iscovery PK 008 Osaka, Japan May 0, 008 O.R. Zaïane 008