Agrawal et al, Mining sequential patterns, Data Eng., 1995

1. Mining Sequential Patterns Rakesh Agrawal, Ramakrishana Srikant (1995) IBM Almaden Research Center 650 Harry Road, San Jose, CA 95120 데이터 연구실이세린 지도 교수 박종수 2014. 3. 28

2. Contents • Abstract • Introduction • Finding Sequential Patterns • The Sequence Phase • Performance • Conclusions and Future Work

3. Abstract • Introduces the problem of mining sequential patterns over a large database. • Presents 3 algorithms to solve this problem. • Shows their results of performance and scale-up experiments.

4. 1. Introduction • 1.1 Problem Statement • The problem of mining sequential patterns is to find the maximal sequences among all sequences that have a certain user-specified minimum support. • Each such maximal sequence represents a sequential pattern.

5. 1. Introduction • 1.2 Related Work • R. Agrawal, T. Imielinski, and A. Swami, “Mining association rules between sets of items in large databases” (1993) • T. G. Dietterich and R. S. Michalski, “Discovering patterns in sequences of events, Artificial Intelligence” (1985) • A. Califano and I. Rigoutsos, “Flash: A fast look-up algorithm for string homology” (1993) • S. Wu and U. Manber, “Fast text searching allowing errors” (1992) • M. Waterman, “Mathematical Methods for DNA Sequence Analysis” (1989) • S. Altschul, W. Gish, W. Miller, E. Myers, and D. Lipman, “A basic local alignment search tool” (1990) • M. Roytberg, “Computer Applications in the Biosciences: A search for common patterns in many sequences” (1992) • M. Vingron and P. Argos, “Computer Applications in the Biosciences: A fast and sensitive multiple sequence alignment algorithm” (1992) • J. T.-L. Wang, G.-W. Chrin, T. G. Marr, B. Shapiro, D. Shasha, and K. Zhang. “Combinatorial pattern discovery for scientific data: Some preliminary results” (1994)

6. 1. Introduction • 1.2 Related Work • Finding of items bought together in a transaction. (Intra-transaction patterns) • AI prediction of the sequential pattern. • Finding matches for pattern in text subsequences. • Discovering similarities in a database of genetic sequences. Comparison

7. 1. Introduction • 1.2 Related Work

8. 1. Introduction • 1.3 Organization of the Paper • Section 2. Gives this problem decomposition. • Section 3. Examines the sequence phase in detail and presents algorithms for this phase. • Section 4. Empirically evaluate the performance of these algorithms and study their scale-up properties. • Section 5. conclusion - summary and directions for future work.

9. Terminology

10. 2. Finding Sequential Patterns • 2.1 The Algorithm • 1. Sort Phase • Converts the original transaction database into a database of customer sequences.

11. 2. Finding Sequential Patterns • 2.1 The Algorithm • 2. Litemset Phase • Find the set of all litemsets L including the set of all 1-sequences. • The set of litemsets is mapped to a set of contiguous integers.

12. 2. Finding Sequential Patterns • 2.1 The Algorithm • 3. Transformation Phase • To process repetitive determination in the following step faster, • Each transaction is replaced by the set of all litemsets contained in that transaction.

13. 2. Finding Sequential Patterns • 2.1 The Algorithm • 4. Sequence Phase • Use the set of litemsets to find the desired sequences. • 5. Maximal Phase • Find the maximal sequences among the set of large sequences.

14. 3. The Sequence Phase • Make multiple passes over the data to generate candidate sequences from seed set of large sequences. 25% (Support > 1.25)

15. 3. The Sequence Phase • 2 Families of algorithms Count-all AprioriAll Count-some AprioriSome DynamicSome

16. 3. The Sequence Phase ① • 3.1 Algorithm AprioriAll ② ③

17. 3. The Sequence Phase • 3.1 Algorithm AprioriAll • 3.1.1 Apriori Candidate Generation p q Join

18. 3. The Sequence Phase • 3.2 Algorithm AprioriSome

19. 3. The Sequence Phase • 3.2 Algorithm AprioriSome • In the forward pass, we only count sequences of certain lengths. Forward phase length6 length2 length3 length4 length5 length1 Backward phase • Forward phase procedure pruning pruning …

20. 3. The Sequence Phase • 3.2 Algorithm AprioriSome • Next() takes as parameter the length of sequences counted in the last pass and returns the length of sequences to be counted in the next pass.

21. 3. The Sequence Phase • 3.3 Algorithm DynamicSome * Backward phase is same as AprioriSome. If step = 3, After initialization of 1, 2, 3, Generate 6, 9, 12 … Has to be initialized

22. 3. The Sequence Phase • 3.3 Algorithm DynamicSome … AprioriAll … AproriSome … DynamicSome

23. 3. The Sequence Phase • 3.3 Algorithm DynamicSome otf-generates (On-the-fly) generates more candidates than apriori-generate. Avoid overlapping

24. 3 Algorithm Example • AprioriAll / AprioriSome / DynamicSome ①

25. 3 Algorithm Example • AprioriAll ②

26. 3 Algorithm Example • AprioriSome ②

27. 3 Algorithm Example • AprioriSome ③

28. 3 Algorithm Example • DynamicSome ② (step = 2)

29. 3 Algorithm Example • DynamicSome ③

30. 4. Performance • 4.1 Generation of Synthetic Data • Customer-sequence sizes are typically clustered around a mean and a few customers may have many transactions. • Transactionsizes are usually clustered around a mean and a few transactions have many items. • Setting: = 5,000 = 25,000N = 10,000

31. 4. Performance • 4.2 Relative Performance • Decreased support by 1% to 0.2%.

32. 4. Performance • 4.2 Relative Performance • Observation: • Execution time support • DynamicSome performs worse. • AprioriSome shows:

33. 4. Performance • 4.3 Scale-up • Scale-up experiments for the AprioriSome algorithm. (AprioriSome and AprioriAll results to be very similar.)

34. 4. Performance • 4.3 Scale-up

35. 5. Conclusions and Future Work • Introduced a new problem of mining sequential patterns from a database of customer sales transactions. • Presented 3 algorithms for solving this problem. • AprioriSome and AprioriAll have comparable performance. • AprioriSome performs a little better for the lower values of the minimum number of customers that must support a sequential pattern. • Both scale linearly with the number of customer transactions. • Both have excellent scale-up properties with respect to the number of transactions in a customer sequence and the number of items in a transaction. • AprioriAll is preferred in some cases that need detail counts of the number of people.

36. 5. Conclusions and Future Work In the future, • Extension of the algorithms to discover sequential patterns across item categories. • Transposition of constraints into the discovery algorithms. There could be item constraints or time constraints.

37. Thank You 