Periodic pattern mining
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The document presents a discussion on periodic pattern mining in time series databases, focusing on key concepts such as time-series definitions, various forms of periodicity, and techniques for detecting these patterns using suffix trees. It covers algorithms proposed for segment and symbol periodicity detection, highlighting their complexities and potential improvements. Additionally, it references existing literature and proposes an algorithm with better efficiency than previous works.
Periodic pattern mining
- 1. 1 I NAME OF PRESENTER Periodic Pattern Mining in Time Series Databases Ashis Kumar Chanda Swapnil Saha Department of Computer Science and Engineering University of Dhaka
- 2. 2 I NAME OF PRESENTERCSE, DU2 Introduction Key Terms Suffix Tree Generation Conclusion > > > Time Series Database> Periodic Pattern Detection > Topics to be covered >
- 3. 3 I NAME OF PRESENTERCSE, DU3 Introduction What is a time-series database? A time-series database consists of sequences of values or events obtained over repeated measurements of time A fixed time intervals (e.g., hourly, daily, weekly).
- 4. A time series is a set of observation taken at specified times A time series involving a variable Y If a time series is defined by y1, y2, y3 ... Values at times t1, t2, t3 ... Then we can write a function of time Y=F(t) 4
- 5. Long term movements Cyclic movements Seasonal movements Irregular or random movements We can define each movements as L, C, S, I variables respectively And Time series variables Y = L+C+S+I or Y = L*C*S*I 5
- 6. Symbol periodicity axy apq amn Sequence periodicity abxy abpq abmn Segment periodicity abxy abxy abxy 6
- 7. Perfect Periodicity abxy abpq abmn abxy acpq abmn Here conf( 4,0, ab)= 2/3 = 0.67 7
- 8. Periodicity in Subsection of a Time Series T= gbxy asdf abpq abmn Stpos = 8 endPos= 15 So, Subsection part gbxy asdf abpq abmn 8
- 9. Periodicity with Time Tolerance We can’t get always noise free time series data So we check some more bit then our target sequence This extra bit is known as time tolerance (tt) If X is a pattern of p length in T then we check At stPos, stPos+p±tt, stPos+2p±tt . . . .. 9
- 10. A period in a time series may be represented by 5 tuple ( S, p, stPos, endPos, Conf) S = sequence of periodic pattern p = check pattern after p num of char Conf= confidence stPos, endPos is the starting and ending position of segment where match pattern 10
- 11. Suppose, T= abxy acpq abdd abmn then ( ab, 4, 0, 11, 1) means Find ab pattern in T from 0 position to 11 postion affter 4 char a b x y a c p q a b d d abmn 0 1 2 3 4 5 6 7 8 9 10 11 11
- 12. Occurrence Vector: a b c a b b a b b a $ 0 1 2 3 4 5 6 7 8 9 Occurrence vector of a : (0 3 6 9) Occurrence vector of ab : (0 3 6) 12
- 13. Difference Vector: a b c a b b a b b a $ 0 1 2 3 4 5 6 7 8 9 Occurrence vector of a : 0 3 Difference vector : 3 Occurrence vector of bb : 4 7 Difference vetor : 3 13
- 14. How to get a string format from a Transactional database? 14 Discretization Technique
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- 16. We need to define a range or group from DB and characterized each range by a unique ASCII character Suppose, In our previous example, log in defined by a log out ,, x before log in ,, b before log out ,, c after log out ,, d 16
- 17. 17
- 18. 18 accx acxd axdd bacx
- 19. ‘abcabbaabb$’ has following ten suffixes. We can ignore the 10th suffix when generating suffix tree 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 6. babb$ 7. abb$ 8. bb$ 9. b$ 10. $ 19
- 21. Strings: 1. abcabbabb$ 2. bcabbabb$ 21 a b a c b b a b b $ b c b a b $ a b b
- 22. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 22 a b a c b b a b b $ b c b a b $ a b b c b a b $ a b b
- 23. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 23 a b b c b a b $ a b b c b a b $ a b b a c b b a b b $
- 24. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 24 a b b c b a b $ a b b c b a b $ a b b a c b b a b b $ b a b b $
- 25. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 25 a b b c b a b $ a b b a c b b a b b $ b a b b $ c b a b $ a b b b a b b $
- 26. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 6. babb$ 26 a b b c b a b $ a b b a c b b a b b $ b a b b $ c b a b $ a b b b a b b $ a b b $
- 27. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 6. babb$ 7. abb$ 27 a b b c b a b $ a b b a c b b a b b $ b a b b $ c b a b $ a b b b a b b $ a b b $ $
- 28. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 6. babb$ 7. abb$ 8. bb$ 28 a b b c b a b $ a b b a c b b a b b $ b a b b $ c b a b $ a b b b a a b b $ $ b b $ $
- 29. Strings: 1. abcabbabb$ 2. bcabbabb$ 3. cabbabb$ 4. abbabb$ 5. bbabb$ 6. babb$ 7. abb$ 8. bb$ 9. b$ 29 a b b c b a b $ a b b a c b b a b b $ b a b b $ c b a b $ a b b b a a b b $ $ b b $ $ $
- 30. abcabbabb$ Edge leaf node holds a number that represents starting position of the suffix Each intermediate node holds a number which is the length of the substring read from root to the intermediate node 30 0 a b 1 b c b a b $ a b b 2a c b b a b b $ 2 6 b a b b $ c b a b $ a b b 1 4 b a 5 a b b $ 3 $ 3 b b $ 2 7 $ $ 8
- 31. abcabbabb$ Find Occrrence Vector 31 0 a b 1 b c b a b $ a b b 2a c b b a b b $ 2 6 b a b b $ c b a b $ a b b 1 4 b a 5 a b b $ 3 $ 3 b b $ 2 7 $ $ 8(3,6)
- 32. abcabbabb$ Find Occrrence Vector 32 0 a b 1 b c b a b $ a b b 2a c b b a b b $ 2 6 b a b b $ c b a b $ a b b 1 4 b a 5 a b b $ 3 $ 3 b b $ 2 7 $ $ 8(3,6) (0,3,6)
- 33. abcabbabb$ Find Occrrence Vector 33 0 a b 1 b c b a b $ a b b 2a c b b a b b $ 2 6 b a b b $ c b a b $ a b b 1 4 b a 5 a b b $ 3 $ 3 b b $ 2 7 $ $ 8(3,6) (0,3,6) (4,7) (1,5,8,4,7)
- 34. Input: a time series of Size n Output: Positions of periodic patterns Process: for each occurrence vector of size k find p for 0 to k check each position after p char count confidence add to list if greater than threshold 34
- 35. abcabbabb$ ab - (0,3,6) abb - (3,6) bb - (4,7) b - (1,5,8,4,7) 35 stpos= 0 endPos= 6 P= 3-0 = 3 Now check occurrence vector of ab if difference equal p count increment Check confidence Add to pattern list if confidence >= Θ
- 36. abcdabcabcab$ ab - (0,4,7,10) 36 stpos= 0 endPos= 10 P= 4-0 = 4 Now check occurrence vector of ab if difference equal p count increment Only one pattern get 0 to 10 with p=4 abcdabcabcab$
- 37. abcdabcabcab$ ab - (0,4,7,10) 37 stpos= 4 endPos= 10 P= 7-4 = 3 Now check occurrence vector of ab if difference equal p count increment 3 pattern get 4 to 10 with p=3 abcdabcabcab$
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- 39. - Elfeky proposed two separate algorithms to detect symbol & segment periodicity. (CONV) & (WARP) But it not used in sub-sequence & complexity O(nlogn) & O(n^2) - Han’s parper algorithm used in sub-sequence But it need user input 39
- 40. - In this perspective, The algorithm discussed here is better than previous - Complexity O(nlogn) - Works online 40
- 41. 41 I NAME OF PRESENTERCSE, DU41 References - Periodic pattern mining using suffix tree by Rasheed, Al-Shalalfa, & Alhajj, 2011 - Effective periodic pattern mining in time series database by Nishi, Farhan, Samiullah, Jeong - Data Mining Concepts & Techniques by J. Han & M. Kamber - Database system Concept by Abraham Sillberschatz, Korth, Sudarshan
- 42. 42 I NAME OF PRESENTERCSE, DU42 Questions
- 43. 43 I NAME OF PRESENTERCSE, DU43 Thank You