IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v206y2025ics0167947324001919.html
   My bibliography  Save this article

Mean shift-based clustering for misaligned functional data

Author

Listed:
  • Welbaum, Andrew
  • Qiao, Wanli

Abstract

Misalignment often occurs in functional data and can severely impact their clustering results. A clustering algorithm for misaligned functional data is developed, by adapting the original mean shift algorithm in the Euclidean space. This mean shift algorithm is applied to the quotient space of the orbits of the square root velocity functions induced by the misaligned functional data, in which the elastic distance is equipped. Convergence properties of this algorithm are studied. The efficacy of the algorithm is demonstrated through simulations and various real data applications.

Suggested Citation

  • Welbaum, Andrew & Qiao, Wanli, 2025. "Mean shift-based clustering for misaligned functional data," Computational Statistics & Data Analysis, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:csdana:v:206:y:2025:i:c:s0167947324001919
    DOI: 10.1016/j.csda.2024.108107
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001919
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108107?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Jeng‐Min Chiou & Pai‐Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699, September.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. 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.
    4. 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.
    5. Frédéric Ferraty & Nadia Kudraszow & Philippe Vieu, 2012. "Nonparametric estimation of a surrogate density function in infinite-dimensional spaces," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 447-464.
    6. 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.
    7. Charles Bouveyron & Julien Jacques, 2011. "Model-based clustering of time series in group-specific functional subspaces," 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. 5(4), pages 281-300, December.
    8. Aliyari Ghassabeh, Youness, 2015. "A sufficient condition for the convergence of the mean shift algorithm with Gaussian kernel," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 1-10.
    9. Amandine Schmutz & Julien Jacques & Charles Bouveyron & Laurence Chèze & Pauline Martin, 2020. "Clustering multivariate functional data in group-specific functional subspaces," Computational Statistics, Springer, vol. 35(3), pages 1101-1131, September.
    10. Juhyun Park & Jeongyoun Ahn, 2017. "Clustering multivariate functional data with phase variation," Biometrics, The International Biometric Society, vol. 73(1), pages 324-333, March.
    11. 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.
    12. Montero, Pablo & Vilar, José A., 2014. "TSclust: An R Package for Time Series Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i01).
    13. Serban, Nicoleta & Wasserman, Larry, 2005. "CATS: Clustering After Transformation and Smoothing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 990-999, September.
    14. Giorgino, Toni, 2009. "Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i07).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juhyun Park & Jeongyoun Ahn, 2017. "Clustering multivariate functional data with phase variation," Biometrics, The International Biometric Society, vol. 73(1), pages 324-333, March.
    2. 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.
    3. Kim, Joonpyo & Oh, Hee-Seok, 2020. "Pseudo-quantile functional data clustering," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    4. 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.
    5. Xin Wang, 2024. "Clustering of longitudinal curves via a penalized method and EM algorithm," Computational Statistics, Springer, vol. 39(3), pages 1485-1512, May.
    6. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    7. Fabio Centofanti & Antonio Lepore & Biagio Palumbo, 2024. "Sparse and smooth functional data clustering," Statistical Papers, Springer, vol. 65(2), pages 795-825, April.
    8. Zhongnan Jin & Jie Min & Yili Hong & Pang Du & Qingyu Yang, 2024. "Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems," INFORMS Joural on Data Science, INFORMS, vol. 3(2), pages 203-218, October.
    9. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," 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. 8(3), pages 231-255, September.
    10. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    11. 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.
    12. Susana Conde & Shahin Tavakoli & Daphne Ezer, 2024. "Functional regression clustering with multiple functional gene expressions," PLOS ONE, Public Library of Science, vol. 19(11), pages 1-23, November.
    13. Rhoden, Imke & Weller, Daniel & Voit, Ann-Katrin, 2021. "Spatio-temporal dynamics of European innovation: An exploratory approach via multivariate functional data cluster analysis," Ruhr Economic Papers 926, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    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. Carmela Iorio & Gianluca Frasso & Antonio D’Ambrosio & Roberta Siciliano, 2023. "Boosted-oriented probabilistic smoothing-spline clustering of series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1123-1140, October.
    16. Cristina Anton & Iain Smith, 2024. "Model-based clustering of functional data via mixtures of t distributions," 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. 18(3), pages 563-595, September.
    17. Amovin-Assagba, Martial & Gannaz, Irène & Jacques, Julien, 2022. "Outlier detection in multivariate functional data through a contaminated mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    18. 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.
    19. Yifan Zhu & Chongzhi Di & Ying Qing Chen, 2019. "Clustering Functional Data with Application to Electronic Medication Adherence Monitoring in HIV Prevention Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 238-261, July.
    20. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:206:y:2025:i:c:s0167947324001919. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.