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Regularized Generalized Canonical Correlation Analysis

Author

Listed:
  • Michel Tenenhaus

    (HEC Paris - Recherche - Hors Laboratoire - HEC Paris - Ecole des Hautes Etudes Commerciales)

  • Arthur Tenenhaus

    (E3S - Supélec Sciences des Systèmes - Ecole Supérieure d'Electricité - SUPELEC (FRANCE))

Abstract

Regularized generalized canonical correlation analysis (RGCCA) is a generalization of regularized canonical correlation analysis to three or more sets of variables. It constitutes a general framework for many multi-block data analysis methods. It combines the power of multi-block data analysis methods (maximization of well identified criteria) and the flexibility of PLS path modeling (the researcher decides which blocks are connected and which are not). Searching for a fixed point of the stationary equations related to RGCCA, a new monotonically convergent algorithm, very similar to the PLS algorithm proposed by Herman Wold, is obtained. Finally, a practical example is discussed.

Suggested Citation

  • Michel Tenenhaus & Arthur Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Post-Print hal-00609220, HAL.
    • Handle: RePEc:hal:journl:hal-00609220
    DOI: 10.1007/s11336-011-9206-8
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Tenenhaus, Arthur & Philippe, Cathy & Frouin, Vincent, 2015. "Kernel Generalized Canonical Correlation Analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 114-131.
    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. 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).
    10. 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.
    11. 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.
    12. Olivier Ledoit & Michael Wolf, 2019. "Quadratic shrinkage for large covariance matrices," ECON - Working Papers 335, Department of Economics - University of Zurich, revised Dec 2020.
    13. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," 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(2), pages 285-313, June.
    14. 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.
    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. Cruz-Cano, Raul & Lee, Mei-Ling Ting, 2014. "Fast regularized canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 88-100.
    17. Marcela Guachamín & Diana Ramírez‐Cifuentes & Olga Delgado, 2020. "An Uncertainty Thermometer to Measure the Macroeconomic‐Financial Risk in South American Countries," Journal of International Development, John Wiley & Sons, Ltd., vol. 32(6), pages 854-890, August.
    18. 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.
    19. 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.
    20. 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.
    21. Mayr, Kathrin & Teller, Christoph, 2023. "Customer deviance in retailing: Managers’ emotional support and employees’ affective wellbeing," Journal of Retailing and Consumer Services, Elsevier, vol. 72(C).
    22. 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.
    23. Tianpeng Li & Shaocang He & Tingting Shen & Jing Sun & Chenxu Sun & Haoqi Pan & Dehai Yu & Wenxue Lu & Runyao Li & Enshan Zhang & Xuqian Lu & Yuxuan Fan & Guiyue Gao, 2022. "Using One-Step Acid Leaching for the Recovering of Coal Gasification Fine Slag as Functional Adsorbents: Preparation and Performance," IJERPH, MDPI, vol. 19(19), pages 1-16, October.
    24. 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.
    25. 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.

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