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Representation-Constrained Canonical Correlation Analysis: A Hybridization of Canonical Correlation and Principal Component Analyses

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Abstract

The classical canonical correlation analysis is extremely greedy to maximize the squared correlation between two sets of variables. As a result, if one of the variables in the dataset-1 is very highly correlated with another variable in the dataset-2, the canonical correlation will be very high irrespective of the correlation among the rest of the variables in the two datasets. We intend here to propose an alternative measure of association between two sets of variables that will not permit the greed of a select few variables in the datasets to prevail upon the fellow variables so much as to deprive the latter of contributing to their representative variables or canonical variates. Our proposed Representation-Constrained Canonical correlation (RCCCA) Analysis has the Classical Canonical Correlation Analysis (CCCA) at its one end (λ=0) and the Classical Principal Component Analysis (CPCA) at the other (as λ tends to be very large). In between it gives us a compromise solution. By a proper choice of λ, one can avoid hijacking of the representation issue of two datasets by a lone couple of highly correlated variables across those datasets. This advantage of the RCCCA over the CCCA deserves a serious attention by the researchers using statistical tools for data analysis.

Suggested Citation

  • Mishra, SK, 2009. "Representation-Constrained Canonical Correlation Analysis: A Hybridization of Canonical Correlation and Principal Component Analyses," MPRA Paper 12948, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:12948
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    File URL: https://mpra.ub.uni-muenchen.de/12948/1/MPRA_paper_12948.pdf
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    1. Mishra, SK, 2006. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions," MPRA Paper 1005, University Library of Munich, Germany.
    2. Mishra, SK, 2009. "A note on the ordinal canonical correlation analysis of two sets of ranking scores," MPRA Paper 12796, University Library of Munich, Germany.
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    Cited by:

    1. Mishra, SK, 2017. "Are Democratic Regimes Antithetical to Globalization?," MPRA Paper 83321, University Library of Munich, Germany.
    2. repec:spr:psycho:v:82:y:2017:i:2:d:10.1007_s11336-015-9478-5 is not listed on IDEAS

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    Keywords

    Representation; constrained; canonical; correlation; principal components; variates; global optimization; particle swarm; ordinal variables; computer program; FORTRAN;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C89 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other

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