Skip to main content
SpringerLink
Log in

Redundancy Index in Canonical Correlation Analysis with Linear Constraints

  • Conference paper
Measurement and Multivariate Analysis

  • 678 Accesses

Summary

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Cramer, E. M. and Nicewander, W. A. (1979). Some symmetric, invariant measures of multivariate association. Psychornetrika, 44, 1, 43–54.

    Article  MathSciNet  MATH  Google Scholar 

  • Gleason, T. C. (1976). On redundancy in canonical analysis. Psychological Bulletin, 83, 6, 1004–1006.

    Article  Google Scholar 

  • Hotelling, H. (1936). Relations between two sets of variates. Biornetrika, 28, 32 1377.

    Google Scholar 

  • Miller, S. K. (1975). In defense of the general canonical correlation index: reply to Nicewander and Wood. Psychological Bulletin, 82, 2, 207–209.

    Article  Google Scholar 

  • Nicewander, W. A. and Wood, D..A. (1974). Comments on “a general canonical correlation index”. Psychological Bulletin, 81, 1, 92–94.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985). Modern Multivariate Statistical Analysis: A Graduate Course Handbook. American Science Press, INC., Ohio.

    Google Scholar 

  • Stewart, D. and Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70, 160–163.

    Article  Google Scholar 

  • Suzukawa, A. (1997). Statistical inference in a canonical correlation analysis with linear constraints. Journal of the Japan Statistical Society, 27, 1, 93–107.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Obihiro University of Agriculture and Veterinary Medicine, Inada, Obihiro, 080-8555, Japan

    Akio Suzukawa & Nobuhiro Taneichi

Authors
  1. Akio Suzukawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nobuhiro Taneichi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Measurement and Evaluation Program CTL, OISE/UT, The University of Toronto, 252 Bloor Street West, M5S 1V6, Toronto, Ontario, Canada

    Shizuhiko Nishisato (Professor Emeritus) (Professor Emeritus)

  2. Center for Information on Statistical Sciences, The Institute of Statistical Mathematics, 4-6-7 Minami Azabu, 106-8569, Minato-ku, Tokyo, Japan

    Yasumasa Baba (Professor) & Koji Kanefuji (Associate Professor) (Professor) &  (Associate Professor)

  3. Information Complexity & Model Selection Department of Statistics, 336 SMC, The University of Tennessee, 37996-0532, Knoxville, TN, USA

    Hamparsum Bozdogan (McKenzie Professor in Business) (McKenzie Professor in Business)

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Japan

About this paper

Cite this paper

Suzukawa, A., Taneichi, N. (2002). Redundancy Index in Canonical Correlation Analysis with Linear Constraints. In: Nishisato, S., Baba, Y., Bozdogan, H., Kanefuji, K. (eds) Measurement and Multivariate Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65955-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-65955-6_13

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65957-0

  • Online ISBN: 978-4-431-65955-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation