IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v134y2015icp1-18.html
   My bibliography  Save this article

Canonical correlation analysis for irregularly and sparsely observed functional data

Author

Listed:
  • Shin, Hyejin
  • Lee, Seokho

Abstract

Several approaches for functional canonical correlation analysis have been developed to measure the association between paired functional data. However, the existing methods in the literature have been developed for dense and balanced functional data, and they cannot be directly applicable to the situations where the observed curves are recorded in the irregular and sparse fashion. In this paper, we model the associations between paired functional data into a linear mixed-effects model framework by relating two sets of curves using canonical correlation analysis. The proposed approach automatically deals with irregularly or sparsely observed functional data, and brings a new insight into the interpretation of canonical correlation analysis. Numerical studies are carried out to demonstrate finite sample behavior. Two real data applications are provided to illustrate the methodology.

Suggested Citation

  • Shin, Hyejin & Lee, Seokho, 2015. "Canonical correlation analysis for irregularly and sparsely observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 1-18.
    • Handle: RePEc:eee:jmvana:v:134:y:2015:i:c:p:1-18
    DOI: 10.1016/j.jmva.2014.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002280
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.10.001?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. Heungsun Hwang & Kwanghee Jung & Yoshio Takane & Todd Woodward, 2012. "Functional Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 48-64, January.
    2. Dubin, Joel A. & Muller, Hans-Georg, 2005. "Dynamical Correlation for Multivariate Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 872-881, September.
    3. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    4. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
    5. Cupidon, J. & Eubank, R. & Gilliam, D. & Ruymgaart, F., 2008. "Some properties of canonical correlations and variates in infinite dimensions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1083-1104, July.
    6. Eubank, R.L. & Hsing, Tailen, 2008. "Canonical correlation for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1634-1661, September.
    7. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    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. Zhou, Yang & Lin, Shu-Chin & Wang, Jane-Ling, 2018. "Local and global temporal correlations for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 1-14.
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Cho, Min Ho & Kurtek, Sebastian & Bharath, Karthik, 2022. "Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Daniel Vieira de Morais & Maria Angélica Pereira de Carvalho Costa & Marivalda Figueredo Santa Bárbara & Fabiane de Lima Silva & Manuela M Moreira & Cristina Delerue-Mato & Luís Avelino Guimarães Dias, 2018. "Antioxidant, photoprotective and inhibitory activity of tyrosinase in extracts of Dalbergia ecastaphyllum," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-16, November.
    5. Deqing Wang & Yan Xu & Lingyun He & Rongyan Liu, 2018. "Spatial and Temporal Differences in the Relationships between Residents’ Income and Consumption in China: A Dynamic Analysis Using Functional Data Analysis," Sustainability, MDPI, vol. 10(12), pages 1-25, December.

    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. Zhou, Yang & Lin, Shu-Chin & Wang, Jane-Ling, 2018. "Local and global temporal correlations for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 1-14.
    2. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    3. Cho, Haeran & Goude, Yannig & Brossat, Xavier & Yao, Qiwei, 2013. "Modeling and forecasting daily electricity load curves: a hybrid approach," LSE Research Online Documents on Economics 49634, London School of Economics and Political Science, LSE Library.
    4. Zhu, Hanbing & Li, Rui & Zhang, Riquan & Lian, Heng, 2020. "Nonlinear functional canonical correlation analysis via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    5. Alvarez, Agustín & Boente, Graciela & Kudraszow, Nadia, 2019. "Robust sieve estimators for functional canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 46-62.
    6. Ji Yeh Choi & Heungsun Hwang & Michio Yamamoto & Kwanghee Jung & Todd S. Woodward, 2017. "A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 427-441, June.
    7. Ruzong Fan & Hong-Bin Fang, 2022. "Stochastic functional linear models and Malliavin calculus," Computational Statistics, Springer, vol. 37(2), pages 591-611, April.
    8. Shen, Cencheng & Sun, Ming & Tang, Minh & Priebe, Carey E., 2014. "Generalized canonical correlation analysis for classification," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 310-322.
    9. 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.
    10. 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.
    11. Shin, Hyejin, 2008. "An extension of Fisher's discriminant analysis for stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1191-1216, July.
    12. Tengteng Xu & Riquan Zhang & Xiuzhen Zhang, 2023. "Estimation of spatial-functional based-line logit model for multivariate longitudinal data," Computational Statistics, Springer, vol. 38(1), pages 79-99, March.
    13. Chen, Lu-Hung & Jiang, Ci-Ren, 2018. "Sensible functional linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 39-52.
    14. Chen, Xuerong & Li, Haoqi & Liang, Hua & Lin, Huazhen, 2019. "Functional response regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 218-233.
    15. Jiguo Cao & Kunlaya Soiaporn & Raymond J. Carroll & David Ruppert, 2019. "Modeling and Prediction of Multiple Correlated Functional Outcomes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 112-129, March.
    16. S. Barahona & P. Centella & X. Gual-Arnau & M. V. Ibáñez & A. Simó, 2020. "Supervised classification of geometrical objects by integrating currents and functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 637-660, September.
    17. Sang, Peijun & Wang, Liangliang & Cao, Jiguo, 2019. "Weighted empirical likelihood inference for dynamical correlations," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 194-206.
    18. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Cody Carroll & Hans‐Georg Müller & Alois Kneip, 2021. "Cross‐component registration for multivariate functional data, with application to growth curves," Biometrics, The International Biometric Society, vol. 77(3), pages 839-851, September.
    20. 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.

    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:jmvana:v:134:y:2015:i:c:p:1-18. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.