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Issue No.12 - December (2010 vol.32)
pp: 2232-2245
Erich Fuchs , University of Passau, Passau
Thiemo Gruber , Univerisity of Applied Sciences, Deggendorf
Jiri Nitschke , University of Passau, Passau
Bernhard Sick , Univerisity of Applied Sciences, Deggendorf
ABSTRACT
The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial—obtained by means of the update steps—can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg—which is suitable for many data streaming applications—offers high accuracy at very low computational costs.
INDEX TERMS
Time series, orthogonal polynomials, least-squares approximation, online segmentation, piecewise polynomial representation, SwiftSeg.
CITATION
Erich Fuchs, Thiemo Gruber, Jiri Nitschke, Bernhard Sick, "Online Segmentation of Time Series Based on Polynomial Least-Squares Approximations", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.32, no. 12, pp. 2232-2245, December 2010, doi:10.1109/TPAMI.2010.44
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