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Canonical correlations in multi-way layout

  • Multivariate Analysis
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Abstract

In this paper, some formulas are proposed, which concern the numbers of unit canonical correlations in a multi-way layout. Different types of canonical correlations are considered and their connection with connectedness and orthogonality are examined.

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References

  • Baksalary, J. K., Puntanen, S. and Yanai, H. (1992). Canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix,Linear Algebra and Its Applications,176, 61–74.

    Article  MATH  MathSciNet  Google Scholar 

  • Bérubé, J., Hartwig, R. and Styan, G. P. H. (1993). On canonical correlations and the degrees of non-orthogonality in the three-way layout,Statistical Science and Data Analysis: Proceedings of the Third Pacific Area Statistical Conference (eds. K. Matusita, M. L. Puri and T. Hayakawa), 245–252, VSP.

  • Hotelling, H. (1936). Relations between two sets of variates,Biometrika 28, 321–377.

    Article  MATH  Google Scholar 

  • Khatri, C. G. (1976). A note on multiple and canonical correlations for a singular covariance matrix,Psychometrika,41, 465–470.

    Article  MATH  MathSciNet  Google Scholar 

  • Lancaster, P. and Tismenetsky, M. (1984).The Theory of Matrices, Academic Press, Orlando.

    MATH  Google Scholar 

  • Rao, C. G. and Yanai, H. (1979). General definition of a projector, its decomposition and application to statistical problems,Journal of Statistical Planning Inference,3, 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  • Styan, G. P. H. (1983). Schur complements and linear statistical models,Proceedings of the First Tampere Seminar Linear Models, 37–75, Department of Mathematical Sciences, University of Tampere.

  • Styan, G. P. H. (1986). Canonical correlations in the three-way layout,Pacific Statistical Congress (eds. I. S. Francis, B. F. J. Manly and F. C. Lam), 433–438, North-Holland, Amsterdam.

    Google Scholar 

  • Yanai, H. and Takane, Y. (1992). Canonical correlation analysis with linear constraints,Linear Algebra and Its Applications,176, 75–89.

    Article  MATH  MathSciNet  Google Scholar 

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Adam, M., Maroulas, J. Canonical correlations in multi-way layout. Ann Inst Stat Math 56, 655–666 (2004). https://doi.org/10.1007/BF02506481

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  • DOI: https://doi.org/10.1007/BF02506481

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