1

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

3 Example: Stock charts Database of time-series

4 Example: Stock charts Database of time-seriesPattern

5 Example: Stock charts Database of time-seriesPatternRetrieval results

6 Example: Stock charts Database of time-seriesPatternRetrieval results

7 Example: Electrocardiogram Database of time-series

8 Example: Electrocardiogram Database of time-seriesPattern

9 Example: Electrocardiogram Database of time-seriesPatternRetrieval results

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. Original series Example:

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

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

23 Definition of important points Important minimum

24 Definition of important points Important minimum a m is the minimum among a i,…, a j

25 Definition of important points Important minimum a m is the minimum among a i,…, a j a i /a m  R and a j /a m  R

26 Definition of important points Important minimum a m is the minimum among a i,…, a j a i /a m  R and a j /a m  R R is a knob that determines compression rate

27 Definition of important points Important maximum a m is the maximum among a i,…, a j a m /a i  R and a m /a j  R R is a knob that determines compression rate

28 Compression example Original series

29 Compression example Original series Compressed series

30 Compression example Original series Compressed series

31 Compression example Original series Compressed series

32 Compression algorithm Linear time Constant memory Accepts streaming data For a series with n values, compression time is  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-seriesPattern

38 Example: Stock charts Database of time-seriesPattern

39 Example: Stock charts Database of time-seriesPattern

40 Example: Stock charts Database of time-seriesPatternRetrieval results

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: n 2 /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

51 Retrieval accuracy: Stock charts 20 % candidates C = 3 10 % C = 2 5 % C = % C = 1.1

52 Retrieval accuracy: Wind speeds 20 % candidates C = % C = % C = 1.1

53 Retrieval candidate quality Stock charts (5,400 legs)447 Air and sea temperatures (5,500 legs)456 Wind speeds (10,500 legs)379 Candidates 5%10%20% Found matches among ten best:

54 Outline Previous work Important points Indexing and retrieval Empirical results Conclusions

55 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

56 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

57 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 ~

58 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 ~

59 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 ~

60 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 ~ ~

61 Main results Compression Fast compression procedure Preserves similarity Retrieval Works with compressed data Controlled trade-off between speed and accuracy