Redundancy Index in Canonical Correlation Analysis with Linear Constraints

  • Akio Suzukawa
  • Nobuhiro Taneichi
Conference paper


The redundancy index proposed by Stewart and Love (1968) is an index to measure the degree to which one set of variables can predict another set of variables, and is associated with canonical correlation analysis. Yanai and Takane (1992) developed canonical correlation analysis with linear constraints (CCALC). In this paper we define a redundancy index in CCALC, which is based on the reformulation of CCALC by Suzukawa (1997). The index is a general measure to summarize redundancy between two sets of variables in the sense that various dependency measures can be obtained by choosing constraints suitably. The asymptotic distribution of the index is derived under normality.


Asymptotic Distribution Linear Constraint Canonical Correlation Canonical Correlation Analysis Canonical Variate 
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  1. Cramer, E. M. and Nicewander, W. A. (1979). Some symmetric, invariant measures of multivariate association. Psychornetrika, 44, 1, 43–54.MathSciNetCrossRefMATHGoogle Scholar
  2. Gleason, T. C. (1976). On redundancy in canonical analysis. Psychological Bulletin, 83, 6, 1004–1006.CrossRefGoogle Scholar
  3. Hotelling, H. (1936). Relations between two sets of variates. Biornetrika, 28, 32 1377.Google Scholar
  4. Miller, S. K. (1975). In defense of the general canonical correlation index: reply to Nicewander and Wood. Psychological Bulletin, 82, 2, 207–209.CrossRefGoogle Scholar
  5. Nicewander, W. A. and Wood, D..A. (1974). Comments on “a general canonical correlation index”. Psychological Bulletin, 81, 1, 92–94.CrossRefGoogle Scholar
  6. Nicewander, W. A. and Wood, D. A. (1975). On the mathematical bases of the general canonical correlation index: rejoinder to Miller. Psychological Bulletin, 82, 2, 210–212.CrossRefGoogle Scholar
  7. Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985). Modern Multivariate Statistical Analysis: A Graduate Course Handbook. American Science Press, INC., Ohio.Google Scholar
  8. Stewart, D. and Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70, 160–163.CrossRefGoogle Scholar
  9. Suzukawa, A. (1997). Statistical inference in a canonical correlation analysis with linear constraints. Journal of the Japan Statistical Society, 27, 1, 93–107.MathSciNetCrossRefMATHGoogle Scholar
  10. Yanai, H. and Takane, Y. (1992). Canonical correlation analysis with linear constraints. Linear Algebra and its Applications, 176, 75–89.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Akio Suzukawa
    • 1
  • Nobuhiro Taneichi
    • 1
  1. 1.Obihiro University of Agriculture and Veterinary MedicineInada, ObihiroJapan

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