IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v133y2015icp356-376.html
   My bibliography  Save this article

A robust predictive approach for canonical correlation analysis

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002048
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.09.007?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. Reinhard Furrer & Marc G. Genton, 2011. "Aggregation-cokriging for highly multivariate spatial data," Biometrika, Biometrika Trust, vol. 98(3), pages 615-631.
    2. Jos Berge, 1979. "On the equivalence of two oblique congruence rotation methods, and orthogonal approximations," Psychometrika, Springer;The Psychometric Society, vol. 44(3), pages 359-364, September.
    3. Peter Filzmoser & Catherine Dehon & Christophe Croux, 2000. "Outlier resistant estimators for canonical correlation analysis," ULB Institutional Repository 2013/8460, ULB -- Universite Libre de Bruxelles.
    4. 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.
    5. Cristophe Croux & Catherine Dehon, 2003. "Estimators of the multiple correlation coefficient: Local robustness and confidence intervals," Statistical Papers, Springer, vol. 44(3), pages 315-334, July.
    6. Mario Romanazzi, 1992. "Influence in canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 237-259, June.
    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. 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.

    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. 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.
    2. 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.
    3. Bachoc, François & Genton, Mark G. & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2019. "Spatial Blind Source Separation," TSE Working Papers 19-998, Toulouse School of Economics (TSE).
    4. Seokhyun Chung & Raed Al Kontar & Zhenke Wu, 2022. "Weakly Supervised Multi-output Regression via Correlated Gaussian Processes," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 115-137, October.
    5. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    6. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    7. Davy Paindaveine & Germain Van Bever, 2017. "Halfspace Depths for Scatter, Concentration and Shape Matrices," Working Papers ECARES ECARES 2017-19, ULB -- Universite Libre de Bruxelles.
    8. Iaci, Ross & Sriram, T.N., 2013. "Robust multivariate association and dimension reduction using density divergences," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 281-295.
    9. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    10. Ella Roelant & Stefan Aelst & Gert Willems, 2009. "The minimum weighted covariance determinant estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(2), pages 177-204, September.
    11. Antonio Punzo & Salvatore Ingrassia & Antonello Maruotti, 2021. "Multivariate hidden Markov regression models: random covariates and heavy-tailed distributions," Statistical Papers, Springer, vol. 62(3), pages 1519-1555, June.
    12. 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.
    13. Hallin Marc & Paindaveine Davy, 2006. "Parametric and semiparametric inference for shape: the role of the scale functional," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 1-24, December.
    14. Cristophe Croux & Catherine Dehon, 2003. "Estimators of the multiple correlation coefficient: Local robustness and confidence intervals," Statistical Papers, Springer, vol. 44(3), pages 315-334, July.
    15. Hallin, Marc & Paindaveine, Davy, 2009. "Optimal tests for homogeneity of covariance, scale, and shape," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 422-444, March.
    16. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
    17. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    18. Paindaveine, Davy & Van Bever, Germain, 2014. "Inference on the shape of elliptical distributions based on the MCD," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 125-144.
    19. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    20. Šárka Hudecová & Miroslav Šiman, 2021. "Testing symmetry around a subspace," Statistical Papers, Springer, vol. 62(5), pages 2491-2508, October.

    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:133:y:2015:i:c:p:356-376. 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.