Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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UNIFYING STATIONARY EQUATIONS FOR GENERALIZED CANONICAL CORRELATION ANALYSIS

  • Published : 2006.06.01
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Abstract

In the present paper, various solutions for generalized canonical correlation analysis (GCCA) are considered depending on the criteria and constraints. For the comparisons of some characteristics of the solutions, we provide with certain unifying stationary equations which might to also useful to obtain various generalized canonical correlation analysis solutions. In addition, we suggest an approach for the generalized canonical correlation analysis by exploiting the concept of maximum eccentricity originally de-signed to test the internal independence structure. The solutions, including new one, are compared through unifying stationary equations and by using some numerical illustrations. A type of iterative procedure for the GCCA solutions is suggested and some numerical examples are provided to illustrate several GCCA methods.

Keywords

References

  1. CARROLL, J. D. (1968). 'Generalization of canonical correlation analysis to three or more sets of variables', Proceedings of the American Psychological Association, 3 227-228
  2. COPPI, R. AND BOLASCO, S. (1989). Multiway Data Analysis, North-Holland, Amsterdam
  3. GIFI, A. (1990). Nonlinear Multivariate Analysis, John Wiley & Sons, Chichester
  4. HORST, P. (1961a). 'Relations among m sets of measures', Psychometrika 26, 129-149 https://doi.org/10.1007/BF02289710
  5. HORST, P. (1961b). 'Generalized canonical correlations and their applications to experimental data', Journal of Clinical Psychology, 17, 331-347 https://doi.org/10.1002/1097-4679(196110)17:4<331::AID-JCLP2270170402>3.0.CO;2-D
  6. HORST, P. (1965). Factor Analysis of Data Matrices, Holt, Rinehart and Winston, New York
  7. HOTELLING, H. (1936). 'Relations between two sets of variates', Biometrika, 28, 321-377 https://doi.org/10.1093/biomet/28.3-4.321
  8. KETTENRING, J. R. (1971). 'Canonical analysis of several sets of variables', Biometrika, 58, 433-451 https://doi.org/10.1093/biomet/58.3.433
  9. LEBART, L., MORINEAU, A. AND WARWICK, K. (1984). Multivariate Descriptive Statistical Analysis. Correspondence Analysis and Related Techniques for Large Matrices, John Wiley & Sons, New York
  10. MAGNUS, J. R. AND NEUDECKER, H. (1988). Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons, Chichester
  11. MELZER, T., REITER, M. AND BISCHOF, H. (2001). 'Nonlinear feature extraction using generalized canonical correlation analysis', Proceedings of the International Conference on Artificial Neural Networks, 353-360
  12. SCHUENEMEYER, J. H. AND BARGMANN R. E. (1978). 'Maximum eccentricity as a unionintersection test statistic in multivariate analysis', Journal of Multivariate Analysis, 8, 268-273 https://doi.org/10.1016/0047-259X(78)90078-7
  13. STEEL, R. G. D. (1951). 'Minimum generalized variance for a set of linear functions', The Annals of Mathematical Statistics, 22, 456-460 https://doi.org/10.1214/aoms/1177729594
  14. TAKANE, Y. AND HWANG, H. (2002). 'Generalized constrained canonical correlation analysis', Multivariate Behavioral Research, 37, 163-195 https://doi.org/10.1207/S15327906MBR3702_01
  15. TEN BERGE, J. M. F. (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
  16. VAN DE GEER, J. P. (1984). 'Linear relations among k sets of variables', Psychometrika, 49, 79-94 https://doi.org/10.1007/BF02294207