IDEAS home Printed from https://ideas.repec.org/a/csb/stintr/v15y2014i2p231-242.html
   My bibliography  Save this article

Methods of Reducing Dimension for Functional Data

Author

Listed:
  • Mirosław Krzyśko
  • Waldemar Wołyński
  • Tomasz Górecki
  • Łukasz Waszak

Abstract

In classical data analysis, objects are characterized by many features observed at one point of time. We would like to present them graphically, to see their configuration, eliminate outlying observations, observe relationships between them or to classify them. In recent years methods for representing data by functions have received much attention. In this paper we discuss a new method of constructing principal components for multivariate functional data. We illustrate our method with data from environmental studies.

Suggested Citation

  • Mirosław Krzyśko & Waldemar Wołyński & Tomasz Górecki & Łukasz Waszak, 2014. "Methods of Reducing Dimension for Functional Data," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(2), pages 231-242, March.
    • Handle: RePEc:csb:stintr:v:15:y:2014:i:2:p:231-242
    as

    Download full text from publisher

    File URL: http://index.stat.gov.pl/repec/files/csb/stintr/csb_stintr_v15_2014_i2_n5.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    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. Mirosław Krzyśko & Peter Nijkamp & Waldemar Ratajczak & Waldemar Wołyński, 2022. "Multidimensional economic indicators and multivariate functional principal component analysis (MFPCA) in a comparative study of countries’ competitiveness," Journal of Geographical Systems, Springer, vol. 24(1), pages 49-65, January.

    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. Mirosław Krzyśko & Łukasz Smaga, 2017. "An Application Of Functional Multivariate Regression Model To Multiclass Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 433-442, September.
    2. Xiuli Du & Xiaohu Jiang & Jinguan Lin, 2023. "Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 975-1001, September.
    3. 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.
    4. 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.
    5. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    6. Tomasz Górecki & Mirosław Krzyśko & Łukasz Waszak & Waldemar Wołyński, 2018. "Selected statistical methods of data analysis for multivariate functional data," Statistical Papers, Springer, vol. 59(1), pages 153-182, March.
    7. Jia Guo & Shiyan Ma & Xiang Li, 2022. "Exploring the Differences of Sustainable Urban Development Levels from the Perspective of Multivariate Functional Data Analysis: A Case Study of 33 Cities in China," Sustainability, MDPI, vol. 14(19), pages 1-19, October.
    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. 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.
    10. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate 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. 17(2), pages 323-345, June.
    11. 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.
    12. T. Górecki & Ł. Smaga, 2017. "Multivariate analysis of variance for functional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2172-2189, September.
    13. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    14. Górecki Tomasz & Krzyśko Mirosław & Ratajczak Waldemar & Wołyński Waldemar, 2016. "An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 449-466, September.
    15. Virta, Joni & Li, Bing & Nordhausen, Klaus & Oja, Hannu, 2020. "Independent component analysis for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    16. Gertheiss, Jan & Goldsmith, Jeff & Staicu, Ana-Maria, 2017. "A note on modeling sparse exponential-family functional response curves," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 46-52.
    17. Rodolfo Metulini & Maurizio Carpita, 2021. "A Spatio-Temporal Indicator for City Users Based on Mobile Phone Signals and Administrative Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 761-781, August.
    18. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    19. 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.
    20. Górecki Tomasz & Krzyśko Mirosław & ński Waldemar Woły, 2019. "Variable Selection In Multivariate Functional Data Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 123-138, June.

    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:csb:stintr:v:15:y:2014:i:2:p:231-242. 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: Beata Witek (email available below). General contact details of provider: https://edirc.repec.org/data/gusgvpl.html .

    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.