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k-mean alignment for curve clustering

Author

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  • 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

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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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    3. Simone Vantini, 2012. "On the definition of phase and amplitude variability in functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 676-696, December.
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    5. Daniel Gervini & Patrick A. Carter, 2014. "Warped functional analysis of variance," Biometrics, The International Biometric Society, vol. 70(3), pages 526-535, September.
    6. Huaihou Chen & Donglin Zeng, 2014. "Comment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1350-1353, December.
    7. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    8. Juhyun Park & Jeongyoun Ahn, 2017. "Clustering multivariate functional data with phase variation," Biometrics, The International Biometric Society, vol. 73(1), pages 324-333, March.
    9. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    10. Slaets, Leen & Claeskens, Gerda & Hubert, Mia, 2012. "Phase and amplitude-based clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2360-2374.
    11. Dimeglio, Chloé & Gallón, Santiago & Loubes, Jean-Michel & Maza, Elie, 2014. "A robust algorithm for template curve estimation based on manifold embedding," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 373-386.
    12. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    13. Tucker, J. Derek & Wu, Wei & Srivastava, Anuj, 2013. "Generative models for functional data using phase and amplitude separation," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 50-66.
    14. Snježana Majstorović & Kristian Sabo & Johannes Jung & Matija Klarić, 2018. "Spectral methods for growth curve clustering," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 715-737, September.
    15. Piercesare Secchi & Simone Vantini & Valeria Vitelli, 2015. "Analysis of spatio-temporal mobile phone data: a case study in the metropolitan area of Milan," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 279-300, July.
    16. Wu, Zizhen & Hitchcock, David B., 2016. "A Bayesian method for simultaneous registration and clustering of functional observations," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 121-136.
    17. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    18. Lili Wang & Qiulin Xiong & Gaofeng Wu & Atul Gautam & Jianfang Jiang & Shuang Liu & Wenji Zhao & Hongliang Guan, 2019. "Spatio-Temporal Variation Characteristics of PM 2.5 in the Beijing–Tianjin–Hebei Region, China, from 2013 to 2018," IJERPH, MDPI, vol. 16(21), pages 1-20, November.
    19. Marco Grasso & Bianca Maria Colosimo & Fugee Tsung, 2017. "A phase I multi-modelling approach for profile monitoring of signal data," International Journal of Production Research, Taylor & Francis Journals, vol. 55(15), pages 4354-4377, August.
    20. Pedro C. Álvarez-Esteban & Luis A. García-Escudero, 2022. "Robust clustering of functional directional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 181-199, March.
    21. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    22. Galvani, Marta & Torti, Agostino & Menafoglio, Alessandra & Vantini, Simone, 2021. "FunCC: A new bi-clustering algorithm for functional data with misalignment," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    23. Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.
    24. Menafoglio, Alessandra & Petris, Giovanni, 2016. "Kriging for Hilbert-space valued random fields: The operatorial point of view," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 84-94.
    25. Wagner, Heiko & Kneip, Alois, 2019. "Nonparametric registration to low-dimensional function spaces," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 49-63.

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