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General problem. Retrieval of time-series similar to a given pattern . Example: Stock charts. Database of time-series. Example: Stock charts. Database of time-series. Pattern. Example: Stock charts. Database of time-series. Pattern. Retrieval results. Example: Stock charts.
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General problem Retrieval of time-series similar to a givenpattern.
Example: Stock charts Database of time-series
Example: Stock charts Database of time-series Pattern
Example: Stock charts Database of time-series Pattern Retrieval results
Example: Stock charts Database of time-series Pattern Retrieval results .92 .87 .86 .84
Example: Electrocardiogram Database of time-series
Example: Electrocardiogram Database of time-series Pattern
Example: Electrocardiogram Database of time-series Pattern Retrieval results .91 .87 .98 1.0
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions } Contributions
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
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions
Previous work • Feature choice • Similarity metrics • Indexing and retrieval
Previous work: Feature choice • Discrete Fourier transforms • Alphabets • Statistical features • Subsets of points
Previous work: Similarity metrics • Euclidean distance • Bounding rectangles • Envelope count • Aggregate similarity
Previous work: Indexing and retrieval • Advanced techniques: • B-trees • R-trees • KD-trees • VP-trees • Grids • Applied techniques: • Linear search with compression
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions
Important points Choose “important” maxima and minima, and discard the other points.
Important points Choose “important” maxima and minima, and discard the other points. Example: Original series
Important points Choose “important” maxima and minima, and discard the other points. Example: Original series
Important points Choose “important” maxima and minima, and discard the other points. Example: Compressed series Original series
Definition of important points Important minimum
Definition of important points Important minimum • am is the minimum among ai,…, aj
Definition of important points Important minimum • am is the minimum among ai,…, aj • ai/am R andaj/am R
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
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
Compression example Originalseries
Compression example Originalseries Compressed series
Compression example Originalseries Compressed series
Compression example Originalseries Compressed series
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).
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions
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
Example: Stock charts Database of time-series
Example: Stock charts Database of time-series
Example: Stock charts Database of time-series Pattern
Example: Stock charts Database of time-series Pattern
Example: Stock charts Database of time-series Pattern
Example: Stock charts Database of time-series Pattern Retrieval results .92 .87 .86 .84
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
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
Alternative versions • Different prominence definitions • Different similarity metrics • The end-point ratio prominence usually gives the best empirical results.
Extended legs Similar sequence
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
Outline • Previous work • Important points • Indexing and retrieval • Empirical results • Conclusions
Data sets • Stock charts • Air and sea temperatures • Wind speeds • Electroencephalograms • Electrocardiograms
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
Patterns Compressed patterns with 4 to 27 legs Examples:
Retrieval time Retrieval time: 0.07 m k milliseconds m legs in a pattern k candidates