General problem

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(No Transcript)
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General problem
Retrieval of time-series similar to a given
pattern.
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Example Stock charts
Database of time-series
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Example Stock charts
Database of time-series
Pattern
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Example Stock charts
Database of time-series
Pattern
Retrieval results
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Example Stock charts
Database of time-series
Pattern
Retrieval results
.92
.87
.86
.84
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Example Electrocardiogram
Database of time-series
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Example Electrocardiogram
Database of time-series
Pattern
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Example Electrocardiogram
Database of time-series
Pattern
Retrieval results
.91
.87
.98
1.0
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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

Contributions
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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

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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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Previous work

• Feature choice
• Similarity metrics
• Indexing and retrieval

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Previous work Feature choice

• Discrete Fourier transforms
• Alphabets
• Statistical features
• Subsets of points

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Previous work Similarity metrics

• Euclidean distance
• Bounding rectangles
• Envelope count
• Aggregate similarity

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Previous work Indexing and retrieval

• Advanced techniques
• B-trees
• R-trees
• KD-trees
• VP-trees
• Grids
• Applied techniques
• Linear search with compression

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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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Important points
Choose important maxima and minima, and discard
the other points.
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Important points
Choose important maxima and minima, and discard
the other points.
Example
Original series
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Important points
Choose important maxima and minima, and discard
the other points.
Example
Original series
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Important points
Choose important maxima and minima, and discard
the other points.
Example
Compressed series
Original series
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Definition of important points
Important minimum

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Definition of important points
Important minimum

• am is the minimum among ai,, aj

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Definition of important points
Important minimum

• am is the minimum among ai,, aj

• ai/am ? R and aj/am ? R

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Definition of important points
Important minimum

• am is the minimum among ai,, aj

• ai/am ? R and aj/am ? R

• R is a knob that determines compression rate

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Definition of important points
Important maximum

• am is the maximum among ai,, aj

• am/ai ? R and am/aj ? R

• R is a knob that determines compression rate

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Compression example
Original series
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Compression example
Original series
Compressed series
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Compression example
Original series
Compressed series
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Compression example
Original series
Compressed series
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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).

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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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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

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

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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

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Alternative versions

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

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Extended legs
Similar sequence
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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

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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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Data sets

• Stock charts
• Air and sea temperatures
• Wind speeds
• Electroencephalograms
• Electrocardiograms

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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
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Patterns
Compressed patterns with 4 to 27 legs
Examples
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Retrieval time
Retrieval time 0.07 ? m ? k
milliseconds m legs in a pattern k candidates
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Retrieval accuracy Stock charts
20 candidates C 3
10 C 2
5 C 1.5
1 C 1.1
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Retrieval accuracy Wind speeds
20 candidates C 1.5
10 C 1.2
5 C 1.1
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Retrieval candidate quality
Found matches among ten best
Candidates
5 10 20
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
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Outline

• Previous work
• Important points
• Indexing and retrieval
• Empirical results
• Conclusions

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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

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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

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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

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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

?
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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

?
?
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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

?
?

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Main results

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