1. 2 general problem retrieval of time-series similar to a given pattern

1

LOCATING PATTERNS INDISCRETE TIME-SERIES

Kevin B. Pratt

Committee:

Eugene FinkDmitry Goldgof

Rafael Perez

2

General problem

Retrieval of time-series similar to a given pattern.

3

Example: Stock chartsDatabase of time-series

4

Example: Stock chartsDatabase of time-series Pattern

5

Example: Stock chartsDatabase of time-series Pattern Retrieval results

6


.92

.87

.86

.84

7

Example: ElectrocardiogramDatabase of time-series

8

Example: ElectrocardiogramDatabase of time-series Pattern

9

Example: ElectrocardiogramDatabase 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




• 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



• Conclusions

14

Previous work

• Feature choice

• Similarity metrics


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 retrievalAdvanced 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


• Conclusions

19

Important points

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

20

Important points


Original series

Example:

21

Important points


Original series

Example:

22

Important points


Original series

Example:

Compressed series

23

Definition of important points

Important minimum

24


Important minimum• am is the minimum among

ai,…, aj

25



ai,…, aj

• ai/am R and aj/am R

26



ai,…, aj

• ai/am R and aj/am R

• R is a knob that determines

compression rate

27


Important maximum• am is the maximum among ai,

…, aj

• am/ai R and am/aj 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 0.0133 n milliseconds (300 MHz PC, Visual Basic 6.0).

33

Outline

• Previous work


• Indexing and retrieval• Empirical results

• Conclusions

34

RetrievalRetrieval 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


36


37


38


39


40


.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



• 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

PatternsCompressed patterns with 4 to 27 legs

Examples:

50

Retrieval timeRetrieval 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 = 1.5

1 %

C = 1.1

52

Retrieval accuracy: Wind speeds

20 % candidates

C = 1.5

10 %

C = 1.2

5 %

C = 1.1

53

Retrieval candidate quality

Stock charts (5,400 legs) 4 4 7

Air and sea temperatures (5,500 legs) 4 5 6

Wind speeds (10,500 legs) 3 7 9

Candidates

5% 10% 20%

Found matches among ten best:

54

Outline

• Previous work




• Conclusions

55


Gunopulos [2000]:






56


Gunopulos [2000]:






57


Gunopulos [2000]:






~

58


Gunopulos [2000]:






~

59


Gunopulos [2000]:






~

60


Gunopulos [2000]:






~~

61

Main results

Compression

• Fast compression procedure

• Preserves similarity

Retrieval

• Works with compressed data

• Controlled trade-off between speed and accuracy

1. 2 general problem retrieval of time-series similar to a given pattern

Documents