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A robust predictive approach for canonical correlation analysis

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  • Adrover, Jorge G.
  • Donato, Stella M.

Abstract

Canonical correlation analysis (CCA) is a dimension-reduction technique in which two random vectors from high dimensional spaces are reduced to a new pair of low dimensional vectors after applying linear transformations to each of them, retaining as much information as possible. The components of the transformed vectors are called canonical variables. One seeks linear combinations of the original vectors maximizing the correlation subject to the constraint that they are to be uncorrelated with the previous canonical variables within each vector. By these means one actually gets two transformed random vectors of lower dimension whose expected square distance has been minimized subject to have uncorrelated components of unit variance within each vector. Since the closeness between the two transformed vectors is evaluated through a highly sensitive measure to outlying observations as the mean square loss, the linear transformations we are seeking are also affected. In this paper we use a robust univariate dispersion measure (like an M-scale) based on the distance of the transformed vectors to derive robust S-estimators for canonical vectors and correlations. An iterative algorithm is performed by exploiting the existence of efficient algorithms for S-estimation in the context of Principal Component Analysis. Some convergence properties are analyzed for the iterative algorithm. A simulation study is conducted to compare the new procedure with some other robust competitors available in the literature, showing a remarkable performance. We also prove that the proposal is Fisher consistent.

Suggested Citation

  • Adrover, Jorge G. & Donato, Stella M., 2015. "A robust predictive approach for canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 356-376.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:356-376
    DOI: 10.1016/j.jmva.2014.09.007
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    References listed on IDEAS

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    1. Reinhard Furrer & Marc G. Genton, 2011. "Aggregation-cokriging for highly multivariate spatial data," Biometrika, Biometrika Trust, vol. 98(3), pages 615-631.
    2. Peter Filzmoser & Catherine Dehon & Christophe Croux, 2000. "Outlier resistant estimators for canonical correlation analysis," ULB Institutional Repository 2013/8460, ULB -- Universite Libre de Bruxelles.
    3. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
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    6. Mario Romanazzi, 1992. "Influence in canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 237-259, June.
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    Cited by:

    1. Andrea Bergesio & María Eugenia Szretter Noste & Víctor J. Yohai, 2021. "A robust proposal of estimation for the sufficient dimension reduction problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 758-783, September.
    2. Stan Lipovetsky, 2022. "Canonical Concordance Correlation Analysis," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    3. Jorge G. Adrover & Stella M. Donato, 2023. "Aspects of robust canonical correlation analysis, principal components and association," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 623-650, June.

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