IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i6p1497-1513.html
   My bibliography  Save this article

Functional data classification: a wavelet approach

Author

Listed:
  • Chung Chang
  • Yakuan Chen
  • R. Ogden

Abstract

In recent years, several methods have been proposed to deal with functional data classification problems (e.g., one-dimensional curves or two- or three-dimensional images). One popular general approach is based on the kernel-based method, proposed by Ferraty and Vieu (Comput Stat Data Anal 44:161–173, 2003 ). The performance of this general method depends heavily on the choice of the semi-metric. Motivated by Fan and Lin (J Am Stat Assoc 93:1007–1021, 1998 ) and our image data, we propose a new semi-metric, based on wavelet thresholding for classifying functional data. This wavelet-thresholding semi-metric is able to adapt to the smoothness of the data and provides for particularly good classification when data features are localized and/or sparse. We conduct simulation studies to compare our proposed method with several functional classification methods and study the relative performance of the methods for classifying positron emission tomography images. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Chung Chang & Yakuan Chen & R. Ogden, 2014. "Functional data classification: a wavelet approach," Computational Statistics, Springer, vol. 29(6), pages 1497-1513, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1497-1513
    DOI: 10.1007/s00180-014-0503-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0503-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-014-0503-4?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. Hongxiao Zhu & Philip J. Brown & Jeffrey S. Morris, 2012. "Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models," Biometrics, The International Biometric Society, vol. 68(4), pages 1260-1268, December.
    2. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    3. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    4. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    5. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    2. Chen, Di-Rong & Cheng, Kun & Liu, Chao, 2022. "Framelet block thresholding estimator for sparse functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Adam B. Kashlak & John A. D. Aston & Richard Nickl, 2019. "Inference on Covariance Operators via Concentration Inequalities: k-sample Tests, Classification, and Clustering via Rademacher Complexities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 214-243, February.
    4. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.

    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. Olusola Samuel Makinde, 2019. "Classification rules based on distribution functions of functional depth," Statistical Papers, Springer, vol. 60(3), pages 629-640, June.
    2. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    3. Mousavi, Seyed Nourollah & Sørensen, Helle, 2017. "Multinomial functional regression with wavelets and LASSO penalization," Econometrics and Statistics, Elsevier, vol. 1(C), pages 150-166.
    4. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    5. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    6. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    7. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    8. Fabrizio Maturo & Rosanna Verde, 2023. "Supervised classification of curves via a combined use of functional data analysis and tree-based methods," Computational Statistics, Springer, vol. 38(1), pages 419-459, March.
    9. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    10. Górecki Tomasz & Krzyśko Mirosław & Wołyński Waldemar, 2015. "Classification Problems Based on Regression Models for Multi-Dimensional Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 16(1), pages 97-110, March.
    11. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
    12. Park, Yeonjoo & Simpson, Douglas G., 2019. "Robust probabilistic classification applicable to irregularly sampled functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 37-49.
    13. Joseph, Esdras & Galeano San Miguel, Pedro & Lillo Rodríguez, Rosa Elvira, 2013. "The Mahalanobis distance for functional data with applications to classification," DES - Working Papers. Statistics and Econometrics. WS ws131312, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
    15. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
    16. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
    17. Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast DD-classification of functional data," Statistical Papers, Springer, vol. 58(4), pages 1055-1089, December.
    18. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
    19. Tomasz Górecki & Mirosław Krzyśko & Waldemar Wołyński, 2015. "Classification Problems Based On Regression Models For Multi-Dimensional Functional Data," Statistics in Transition New Series, Polish Statistical Association, vol. 16(1), pages 97-110, March.
    20. Manuel Febrero-Bande, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 35-40, March.

    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:spr:compst:v:29:y:2014:i:6:p:1497-1513. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.