Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Higher-order solutions for generalized canonical correlation analysis

  • Kang, Hyuncheol (Division of Big Data and Management Engineering, Hoseo University)
  • Received : 2019.02.27
  • Accepted : 2019.03.27
  • Published : 2019.05.31
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Abstract

Generalized canonical correlation analysis (GCCA) extends the canonical correlation analysis (CCA) to the case of more than two sets of variables and there have been many studies on how two-set canonical solutions can be generalized. In this paper, we derive certain stationary equations which can lead the higher-order solutions of several GCCA methods and suggest a type of iterative procedure to obtain the canonical coefficients. In addition, with some numerical examples we present the methods for graphical display, which are useful to interpret the GCCA results obtained.

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References

  1. Anderson TW (1984). An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New York.
  2. Carroll JD (1968). Generalization of canonical correlation analysis to three or more sets of variables. In Proceedings of American Psychology Association, 227-228.
  3. Coppi R and Bolasco S (1989). Multiway Data Analysis, North-Holland, New York.
  4. Gifi A (1990). Nonlinear Multivariate Analysis, Wiley, New York.
  5. Horst P (1961a). Relations among m sets of measures, Psychometrika, 26, 129-149. https://doi.org/10.1007/BF02289710
  6. Horst P (1961b). Generalized canonical correlations and their applications to experimental data, Journal of Clinical Psychology (Monograph supplement), 14, 331-347. https://doi.org/10.1002/1097-4679(196110)17:4<331::AID-JCLP2270170402>3.0.CO;2-D
  7. Horst P (1965). Factor Analysis of Data Matrices, Holt, Rinehart and Winston, New York.
  8. Kang H and Kim K (2006). Unifying stationary equations for generalized canonical correlation analysis, Journal of the Korean Statistical Society, 35, 143-156.
  9. Kettenring JR (1971). Canonical analysis of several sets of variables, Biometrika, 58, 433-451. https://doi.org/10.1093/biomet/58.3.433
  10. Park MR and Huh MH (1996). Quantification plots for several sets of variables, Journal of the Korean Statistical Society, 25, 589-601.
  11. Steel GRD (1951). Minimum generalized variance for a set of linear functions, Annals of Mathematical Statistics, 22, 456-460. https://doi.org/10.1214/aoms/1177729594
  12. Ten Berge JMF (1988). Generalized approaches to the MAXBET problem and the MAXDIFF problem, with applications to canonical correlations, Psychometrika, 53, 487-494. https://doi.org/10.1007/BF02294402
  13. Van de Geer JP (1984). Linear relations among k sets of variables, Psychometrika, 49, 79-94. https://doi.org/10.1007/BF02294207