IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v111y2017icp27-47.html
   My bibliography  Save this article

Online EM for functional data

Author

Listed:
  • Maire, Florian
  • Moulines, Eric
  • Lefebvre, Sidonie

Abstract

A novel approach to perform unsupervised sequential learning for functional data is proposed. The goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. The proposed model generalizes the Bayesian dense deformable template model, a hierarchical model in which the template is the function to be estimated and the deformation is a nuisance, assumed to be random with a known prior distribution. The templates are estimated using a Monte Carlo version of the online Expectation–Maximization (EM) algorithm. The designed sequential inference framework is significantly more computationally efficient than equivalent batch learning algorithms, especially when the missing data is high-dimensional. Some numerical illustrations on curve registration problem and templates extraction from images are provided to support the methodology.

Suggested Citation

  • Maire, Florian & Moulines, Eric & Lefebvre, Sidonie, 2017. "Online EM for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 27-47.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:27-47
    DOI: 10.1016/j.csda.2017.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317300191
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.01.006?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Allassonnière, Stéphanie & Kuhn, Estelle, 2015. "Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 4-19.
    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. Moffa, Giusi & Kuipers, Jack, 2014. "Sequential Monte Carlo EM for multivariate probit models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 252-272.
    4. 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.
    5. Liu, Z. & Almhana, J. & Choulakian, V. & McGorman, R., 2006. "Online EM algorithm for mixture with application to internet traffic modeling," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1052-1071, February.
    6. 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.
    7. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    8. Nguyen, Hien D. & McLachlan, Geoffrey J. & Wood, Ian A., 2016. "Mixtures of spatial spline regressions for clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 76-85.
    9. 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.
    10. Olivier Cappé & Eric Moulines, 2009. "On‐line expectation–maximization algorithm for latent data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 593-613, June.
    11. S. Allassonnière & Y. Amit & A. Trouvé, 2007. "Towards a coherent statistical framework for dense deformable template estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 3-29, February.
    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. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    2. 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.
    3. L. Ippel & M. C. Kaptein & J. K. Vermunt, 2019. "Estimating Multilevel Models on Data Streams," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 41-64, March.
    4. Ippel, L. & Kaptein, M.C. & Vermunt, J.K., 2016. "Estimating random-intercept models on data streams," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 169-182.
    5. 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.
    6. Zhang, Zili & Charalambous, Christiana & Foster, Peter, 2023. "A Gaussian copula joint model for longitudinal and time-to-event data with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    7. Arribas-Gil, Ana & Müller, Hans-Georg, 2014. "Pairwise dynamic time warping for event data," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 255-268.
    8. 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.
    9. Donatello Telesca & Lurdes Y.T. Inoue & Mauricio Neira & Ruth Etzioni & Martin Gleave & Colleen Nelson, 2009. "Differential Expression and Network Inferences through Functional Data Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 793-804, September.
    10. Sato, Aki-Hiro, 2012. "Patterns of regional travel behavior: An analysis of Japanese hotel reservation data," International Review of Financial Analysis, Elsevier, vol. 23(C), pages 55-65.
    11. Jason Cleveland & Wei Wu & Anuj Srivastava, 2016. "Norm-preserving constraint in the Fisher--Rao registration and its application in signal estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 338-359, June.
    12. Shuji Shinohara & Nobuhito Manome & Kouta Suzuki & Ung-il Chung & Tatsuji Takahashi & Hiroshi Okamoto & Yukio Pegio Gunji & Yoshihiro Nakajima & Shunji Mitsuyoshi, 2020. "A new method of Bayesian causal inference in non-stationary environments," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-22, May.
    13. Allassonnière, Stéphanie & Kuhn, Estelle, 2015. "Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 4-19.
    14. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
    15. 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.
    16. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Maximum likelihood estimation of triangular and polygonal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 23-36.
    17. Fu, Eric & Heckman, Nancy, 2019. "Model-based curve registration via stochastic approximation EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 159-175.
    18. 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.
    19. Murray, James & Philipson, Pete, 2022. "A fast approximate EM algorithm for joint models of survival and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    20. González, M. & Minuesa, C. & del Puerto, I., 2016. "Maximum likelihood estimation and expectation–maximization algorithm for controlled branching processes," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 209-227.

    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:111:y:2017:i:c:p:27-47. 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.