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k-mean alignment for curve clustering

Author

Listed:
  • Sangalli, Laura M.
  • Secchi, Piercesare
  • Vantini, Simone
  • Vitelli, Valeria

Abstract

The problem of curve clustering when curves are misaligned is considered. A novel algorithm is described, which jointly clusters and aligns curves. The proposed procedure efficiently decouples amplitude and phase variability; in particular, it is able to detect amplitude clusters while simultaneously disclosing clustering structures in the phase, pointing out features that can neither be captured by simple curve clustering nor by simple curve alignment. The procedure is illustrated via simulation studies and applications to real data.

Suggested Citation

  • Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1219-1233
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    References listed on IDEAS

    as
    1. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Veneziani, Alessandro, 2009. "A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 37-48.
    2. Telesca, Donatello & Inoue, Lurdes Y.T., 2008. "Bayesian Hierarchical Curve Registration," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 328-339, March.
    3. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    4. Laura M. Sangalli & Piercesare Secchi & Simone Vantini & Alessandro Veneziani, 2009. "Efficient estimation of three‐dimensional curves and their derivatives by free‐knot regression splines, applied to the analysis of inner carotid artery centrelines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 285-306, July.
    5. Liu, Xueli & Yang, Mark C.K., 2009. "Simultaneous curve registration and clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1361-1376, February.
    6. Daniel Gervini & Theo Gasser, 2004. "Self‐modelling warping functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 959-971, November.
    7. Kaziska, David & Srivastava, Anuj, 2007. "Gait-Based Human Recognition by Classification of Cyclostationary Processes on Nonlinear Shape Manifolds," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1114-1124, December.
    8. Ke C. & Wang Y., 2001. "Semiparametric Nonlinear Mixed-Effects Models and Their Applications," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1272-1298, December.
    9. Cuesta-Albertos, Juan Antonio & Fraiman, Ricardo, 2007. "Impartial trimmed k-means for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4864-4877, June.
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