Application of Symbolic Paa

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APPLICATION OF SYMBOLICAPPLICATION OF SYMBOLIC

PIECEWISE AGGREGATEPIECEWISE AGGREGATEAPPROXIMATION (PAA) ANALYSISAPPROXIMATION (PAA) ANALYSISTO ECG SIGNALSTO ECG SIGNALS

Burcu Klaholu{[email protected]}

Serhan zdemir, Bora . Kumova

Izmir Institute of Technology,Izmir, Turkey


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OutlineOutline

y Past Work

y Symbolic Time Series

y Application of Symbolic PAA Analysis to ECGData Experimental Settings

Steps Applied

Experimental Results Application on a Synthetic Data

y Conclusion

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PastPast workwork

y The studies on Symbolic Time Representationshave emerged in the 1980s.

y Crutchfield introduced computational

mechanical approach into Symbolic Time SeriesAnalysis.

y Ray analyzed symbolic dynamics of complexsystems for anomaly detection. (2003)

y SAX (Symbolic Aggregate Approximation) isinvented by Keogh & Lin (2002)

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SymbolicSymbolic timetime seriesseries

y Huge amounts of data in the form of time-series are available today.

y Symbolic time series provide the end-user asymbolic representation of time-series.

y

The goal is to derive a more compact andexpressive view of large time series thanks to asymbolic representation preserving as muchinformation as possible.

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ApplicationApplication ofof symbolicsymbolic PAAPAA analysisanalysis

toto ECG dataECG datay Experimental Settings:

symbolize a problematic ECG data

measured at 250Hz during 70 seconds.

It consists of 15080 data points

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toto ECG dataECG datay Steps Applied: Noise Seperation - assumed no noise Segmentation Methods:

Symbolization725.06.2008


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toto ECG dataECG data -- SegmentationSegmentationy Segmentation Methods Performed:

It is first proposed to use PLA:x Top-Down

x Sliding Window

x Bottom-Up

x SWAB

Bottom-Up Approach utilized PAA used despite of PLA

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toto ECG dataECG data -- SegmentationSegmentationy PLA with

Merging 15000

Data Points

y PLA withMerging 10000Data Points

y PLA withMerging 14500Data Points

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toto ECG dataECG data -- SymbolizationSymbolizationy SAX:

a symbolization method In order to be able to use SAX; the time series

should be converted into PAA representation

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SAX Keogh & Linn


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toto ECG dataECG data -- SymbolizationSymbolizationy Extended SAX:

Employ min and max points into the symbol string

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Extended SAX - Lkhagva,

Suzuki & Kawagoe


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toto ECG dataECG data PAAPAA andand SAXSAXa if value < 1

symbol = b if 1 < value < 2

c if value > 2

y Euclidean Distance will be used for similaritymeasure:

2211 ......),( nn yxyxyxd !

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toto ECG dataECG data ExperimentalExperimental resultsresultsy Breakpoints 0.9 and 1.2 yield the following symbol

string:aca aca aca bca aca bca bca bca bca bca bca bca cca cca caa cca acabca bca caa caa caa caa cab cab caa cab caa caa cab cab caa cab cabcab cab abc aac bca bca aca aca cab cab cab cab cab cab cac cab cabcac cac cab cab cac cac cac cab cab cab cba aca caa cab cac cac caccab cab

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ApplicationApplication ofof symbolicsymbolic PAAPAA analysisanalysistoto ECG dataECG data ExperimentalExperimental resultsresults

y aca aca aca bca aca bca bca bca bca bca bca bca cca ccacaa cca aca bca bca caa caa caa caa cab cab caa cab caacaa cab cab caa cab cab cab cab abc aac bca bca aca aca

cab cab cab cab cab cab cac cab cab cac cac cab cab caccac cac cab cab cab cba ACA caa cab cac cac cac cabcab

y

There is a symbol shift (bca - cab - abc)y Might be caused by inequal segment sizes

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ApplicationApplication ofof symbolicsymbolic PAAPAA analysisanalysistoto syntheticsynthetic datadata

y A synthetic ECG series with segment size of 74

740 data points

noise with maximum value of 0.1 decreased the value of one segment by 1.0 (anomaly)

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ApplicationApplication ofof symbolicsymbolic PAAPAA analysisanalysistoto syntheticsynthetic datadata

y Obtained symbol string with breakpoints 0.8 and 1.8:

cab cab cab cbb cab cab cab cab baa cbb

y The aim is to have an identifiable error for theanomalous segment than the others

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ConclusionsConclusions

y The error caused by the anomaly is similar to theerror caused by some other parts of the symbolstring.

y This discrepancy is a result of the symbol shiftsthat occur because ECG data has non-equalsegment sizes.

y On an artificially created completely periodic ECGdata, lack of shifts exposes the true anomalies.

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ConclusionsConclusions

y PAA along with extended SAX is not capable ofhandling aperiodic data.

y Why are PAA and SAX are used instead ofother methods?

Seemed to be the most appropriate methodto symbolize time series

New hybrid techniques may be developed tosuit the needs

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ReferencesReferencesy G. Hebrail, B. Hugueney, Symbolic representation of long time

series. Conference on Applied Statistical Models and Data Analysis(ASMDA2001), Compigne, 2001

y A. Ray, Symbolic dynamic analysis of complex systems for anomalydetection, Signal Processing, 84(7), 2004, 11151130.

y E. Keogh, S. Lonardi, B. Chiu, A Symbolic Representation of TimeSeries, with Implications for StreamingAlgorithms, Proc. 8th ACMSIGMOD Workshop on Research Issues in Data Mining andKnowledge Discovery, San Diego, CA, 2003

y B. Lkhagva, Y. Suzuki, K. Kawagoe, Extended SAX: Extension ofsymbolic aggregate approximation for financial time series datarepresentation, DEWS, 2006, 4A-i8.

y E. Keogh, A tutorial on indexing and mining time series data, ICDM'01 The 2001 IEEE International Conference on Data Mining, SanJose

y A. Ray, Anomaly detection and failure migitation in complexdynamical systems, Seminar at National Institute of Standards andTechnology, 2004

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ReferencesReferences ((continuedcontinued))y C. R. Shalizi, K. L. Shalizi, J. P. Crutchfield, Pattern Discovery in Time

Series, Part I: Theory, Algorithm, Analysis, and Convergence, Journalof Machine Learning Research, 2003

y L. Karamitopoulos, G. Evangelidis, Current trends in time seriesrepresentation, A-68, Panhellenic Conference on Informatics (P.C.I.)2007, Patras

y B. Chiu, E. Keogh, S. Lonardi, Probabilistic discovery of time seriesmotifs, Proc. 9th ACM SIGKDD international conference onKnowledge discovery and data mining, Washington D.C., 2003, 493-498

y M. Falk, F. Marohn, R. Michel, D. Hofmann, M. Macke, A First Courseon Time SeriesAnalysis, (Chair of Statistics, University of Wrzburg,

2006)y T. K.Moon, W. C. Stirling, Mathematical methods and algorithms for

signal processing (Prentice Hall, 2000)

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Application of Symbolic Paa

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