IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v90y2015icp114-131.html
   My bibliography  Save this article

Kernel Generalized Canonical Correlation Analysis

Author

Listed:
  • Tenenhaus, Arthur
  • Philippe, Cathy
  • Frouin, Vincent

Abstract

There is a growing need to analyze datasets characterized by several sets of variables observed on a single set of observations. Such complex but structured dataset are known as multiblock dataset, and their analysis requires the development of new and flexible tools. For this purpose, Kernel Generalized Canonical Correlation Analysis (KGCCA) is proposed and offers a general framework for multiblock data analysis taking into account an a priori graph of connections between blocks. It appears that KGCCA subsumes, with a single monotonically convergent algorithm, a remarkably large number of well-known and new methods as particular cases. KGCCA is applied to a simulated 3-block dataset and a real molecular biology dataset that combines Gene Expression data, Comparative Genomic Hybridization data and a qualitative phenotype measured for a set of 53 children with glioma.

Suggested Citation

  • Tenenhaus, Arthur & Philippe, Cathy & Frouin, Vincent, 2015. "Kernel Generalized Canonical Correlation Analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 114-131.
    • Handle: RePEc:eee:csdana:v:90:y:2015:i:c:p:114-131
    DOI: 10.1016/j.csda.2015.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315001012
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.04.004?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Paul Horst, 1961. "Relations amongm sets of measures," Psychometrika, Springer;The Psychometric Society, vol. 26(2), pages 129-149, June.
    3. Michel Tenenhaus & Arthur Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Post-Print hal-00609220, HAL.
    4. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    5. John Geer, 1984. "Linear relations amongk sets of variables," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 79-94, March.
    6. Witten Daniela M & Tibshirani Robert J., 2009. "Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-29, June.
    7. Yoshio Takane & Heungsun Hwang & Hervé Abdi, 2008. "Regularized Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 753-775, December.
    8. Bougeard, S. & Hanafi, M. & Qannari, E.M., 2008. "Continuum redundancy-PLS regression: A simple continuum approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3686-3696, March.
    9. Vinod, H. D., 1976. "Canonical ridge and econometrics of joint production," Journal of Econometrics, Elsevier, vol. 4(2), pages 147-166, May.
    10. Hanafi, Mohamed & Kiers, Henk A.L., 2006. "Analysis of K sets of data, with differential emphasis on agreement between and within sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1491-1508, December.
    11. Michel Tenenhaus, 2011. "Regularized generalized canonical correlation analysis," Post-Print hal-00578321, HAL.
    12. Cruz-Cano, Raul & Lee, Mei-Ling Ting, 2014. "Fast regularized canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 88-100.
    13. Tenenhaus, Arthur & Tenenhaus, Michel, 2014. "Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis," European Journal of Operational Research, Elsevier, vol. 238(2), pages 391-403.
    14. Tenenhaus, Michel & Vinzi, Vincenzo Esposito & Chatelin, Yves-Marie & Lauro, Carlo, 2005. "PLS path modeling," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 159-205, January.
    15. Arthur Tenenhaus & Michel Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 257-284, April.
    16. Takane, Yoshio & Hwang, Heungsun, 2007. "Regularized linear and kernel redundancy analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 394-405, September.
    17. González, Ignacio & Déjean, Sébastien & Martin, Pascal G. P. & Baccini, Alain, 2008. "CCA: An R Package to Extend Canonical Correlation Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i12).
    18. Ledyard Tucker, 1958. "An inter-battery method of factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(2), pages 111-136, June.
    19. Mohamed Hanafi, 2007. "PLS Path modelling: computation of latent variables with the estimation mode B," Computational Statistics, Springer, vol. 22(2), pages 275-292, July.
    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. Dybro Liengaard, Benjamin, 2024. "Measurement invariance testing in partial least squares structural equation modeling," Journal of Business Research, Elsevier, vol. 177(C).
    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.

    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. Michel Tenenhaus & Arthur Tenenhaus & Patrick J. F. Groenen, 2017. "Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 737-777, September.
    2. Arthur Tenenhaus & Michel Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 257-284, April.
    3. Tenenhaus, Arthur & Tenenhaus, Michel, 2014. "Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis," European Journal of Operational Research, Elsevier, vol. 238(2), pages 391-403.
    4. Cruz-Cano, Raul & Lee, Mei-Ling Ting, 2014. "Fast regularized canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 88-100.
    5. Wang, Wenjia & Zhou, Yi-Hui, 2021. "Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    6. Rosaria Romano & Francesco Palumbo, 2021. "Partial possibilistic regression path modeling: handling uncertainty in path modeling," Computational Statistics, Springer, vol. 36(1), pages 615-639, March.
    7. Lukáš Malec & Vladimír Janovský, 2020. "Connecting the multivariate partial least squares with canonical analysis: a path-following approach," 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. 14(3), pages 589-609, September.
    8. Cristina Davino & Pasquale Dolce & Stefania Taralli & Domenico Vistocco, 2022. "Composite-Based Path Modeling for Conditional Quantiles Prediction. An Application to Assess Health Differences at Local Level in a Well-Being Perspective," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 161(2), pages 907-936, June.
    9. Olivier Ledoit & Michael Wolf, 2019. "Quadratic shrinkage for large covariance matrices," ECON - Working Papers 335, Department of Economics - University of Zurich, revised Dec 2020.
    10. Pasquale Dolce & Vincenzo Esposito Vinzi & Natale Carlo Lauro, 2018. "Non-symmetrical composite-based path modeling," 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. 12(3), pages 759-784, September.
    11. Francesca Petrarca & Silvia Terzi, 2018. "The Global Competitiveness Index: an alternative measure with endogenously derived weights," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(5), pages 2197-2219, September.
    12. 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.
    13. Sarstedt, Marko & Hair, Joseph F. & Ringle, Christian M. & Thiele, Kai O. & Gudergan, Siegfried P., 2016. "Estimation issues with PLS and CBSEM: Where the bias lies!," Journal of Business Research, Elsevier, vol. 69(10), pages 3998-4010.
    14. Heungsun Hwang & Gyeongcheol Cho, 2020. "Global Least Squares Path Modeling: A Full-Information Alternative to Partial Least Squares Path Modeling," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 947-972, December.
    15. Joseph F. Hair & G. Tomas M. Hult & Christian M. Ringle & Marko Sarstedt & Kai Oliver Thiele, 2017. "Mirror, mirror on the wall: a comparative evaluation of composite-based structural equation modeling methods," Journal of the Academy of Marketing Science, Springer, vol. 45(5), pages 616-632, September.
    16. Florian Rohart & Benoît Gautier & Amrit Singh & Kim-Anh Lê Cao, 2017. "mixOmics: An R package for ‘omics feature selection and multiple data integration," PLOS Computational Biology, Public Library of Science, vol. 13(11), pages 1-19, November.
    17. Cristina Davino & Vincenzo Esposito Vinzi, 2016. "Quantile composite-based path modeling," 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. 10(4), pages 491-520, December.
    18. Bingsheng Liu & Tengfei Huo & Pinchao Liao & Jie Gong & Bin Xue, 2015. "A Group Decision-Making Aggregation Model for Contractor Selection in Large Scale Construction Projects Based on Two-Stage Partial Least Squares (PLS) Path Modeling," Group Decision and Negotiation, Springer, vol. 24(5), pages 855-883, September.
    19. Husson, François & Josse, Julie & Saporta, Gilbert, 2016. "Jan de Leeuw and the French School of Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i06).
    20. Evermann, Joerg & Tate, Mary, 2016. "Assessing the predictive performance of structural equation model estimators," Journal of Business Research, Elsevier, vol. 69(10), pages 4565-4582.

    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:90:y:2015:i:c:p:114-131. 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.