General problem

2. General problem Retrieval of time-series similar to a givenpattern.

3. Example: Stock charts Database of time-series

4. Example: Stock charts Database of time-series Pattern

5. Example: Stock charts Database of time-series Pattern Retrieval results

6. Example: Stock charts Database of time-series Pattern Retrieval results .92 .87 .86 .84

7. Example: Electrocardiogram Database of time-series

8. Example: Electrocardiogram Database of time-series Pattern

9. Example: Electrocardiogram Database of time-series Pattern Retrieval results .91 .87 .98 1.0

10. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions

11. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions } Contributions

12. Criteria for retrieval methods Gunopulos [2000]: • Work for erratic time-series • Accept any pattern • Find inexact matches • Work when some points are missing • Work on streaming data

13. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions

14. Previous work • Feature choice • Similarity metrics • Indexing and retrieval

15. Previous work: Feature choice • Discrete Fourier transforms • Alphabets • Statistical features • Subsets of points

16. Previous work: Similarity metrics • Euclidean distance • Bounding rectangles • Envelope count • Aggregate similarity

17. Previous work: Indexing and retrieval • Advanced techniques: • B-trees • R-trees • KD-trees • VP-trees • Grids • Applied techniques: • Linear search with compression

18. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions

19. Important points Choose “important” maxima and minima, and discard the other points.

20. Important points Choose “important” maxima and minima, and discard the other points. Example: Original series

21. Important points Choose “important” maxima and minima, and discard the other points. Example: Original series

22. Important points Choose “important” maxima and minima, and discard the other points. Example: Compressed series Original series

23. Definition of important points Important minimum

24. Definition of important points Important minimum • am is the minimum among ai,…, aj

25. Definition of important points Important minimum • am is the minimum among ai,…, aj • ai/am  R andaj/am  R

26. Definition of important points Important minimum • am is the minimum among ai,…, aj • ai/am  R andaj/am  R • R is a knob that determines compression rate

27. Definition of important points Important maximum • am is the maximum among ai,…, aj • am/ai  R andam/aj  R • R is a knob that determines compression rate

28. Compression example Originalseries

29. Compression example Originalseries Compressed series

30. Compression example Originalseries Compressed series

31. Compression example Originalseries Compressed series

32. Compression algorithm • Linear time • Constant memory • Accepts streaming data • For a series with n values, compression time is 0.0133 n milliseconds (300 MHz PC, Visual Basic 6.0).

33. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions

34. Retrieval • Retrieval of time-series similar to a given pattern. • Intuition: • Find a prominent feature in the pattern • Find candidate segments with a similar feature • Compare similarity of candidates to the pattern

35. Example: Stock charts Database of time-series

36. Example: Stock charts Database of time-series

37. Example: Stock charts Database of time-series Pattern

38. Example: Stock charts Database of time-series Pattern

39. Example: Stock charts Database of time-series Pattern

40. Example: Stock charts Database of time-series Pattern Retrieval results .92 .87 .86 .84

41. Algorithm • Identify the prominent leg in the pattern • Retrieve similar legs from the database • Identify corresponding candidate segments • For each candidate segment, compute its similarity to the pattern • Output the candidates whose similarity is above the threshold

42. Important details • Use compressed pattern and compressed sequences in the retrieval process • The prominent feature is the leg having the greatest ratio of right end to left end • All legs in the database are indexed by their prominence, using a binary search tree

43. Alternative versions • Different prominence definitions • Different similarity metrics • The end-point ratio prominence usually gives the best empirical results.

44. Extended legs Similar sequence

45. Indexing on extended legs • Advantage: More accurate retrieval • Disadvantage: Larger index, more memory • If a compressed sequence has n legs: • Worst case: n2/2 extended legs • Average case: (n  lg n) extended legs

46. Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions

47. Data sets • Stock charts • Air and sea temperatures • Wind speeds • Electroencephalograms • Electrocardiograms

48. Data sets • Stock charts • Air and sea temperatures • Wind speeds • Electroencephalograms • Electrocardiograms 60,000 points 445,000 points 79,000 points 17,000 points 2,000 points

49. Patterns Compressed patterns with 4 to 27 legs Examples:

50. Retrieval time Retrieval time: 0.07  m k milliseconds m legs in a pattern k candidates