Research Article Open Access

Optimization of Penalty Parameter in Penalized Nonlinear Canonical Correlation Analysis by using Cross-Validation

Isamu Nagai1
  • 1 Chukyo University, Japan

Abstract

There is Canonical Correlation Analysis (CCA) as a way to find a linear relationship between a pair of random vectors. However, CCA cannot find a nonlinear relationship between them since the method maximizes the correlation between linear combinations of the vectors. In order to find the nonlinear relationship, we convert the vectors through some known conversion functions like a kernel function. Then we find the nonlinear relationship in the original vectors through the conversion function. However, this method has a critical issue in that the maximized correlation sometimes becomes 1 even if there is no relationship between the random vectors. Some author proposed a penalized method with a penalty parameter that avoids this issue when the kernel functions are used for conversion. In this method, however, methods have not been proposed for optimizing the penalty and other hyper parameters in the conversion function, even though the results heavily depend on these parameters. In this study, we propose an optimization method for the penalty and other parameters, based on the simple cross-validation method.

Journal of Mathematics and Statistics
Volume 11 No. 3, 2015, 99-106

DOI: https://doi.org/10.3844/jmssp.2015.99.106

Submitted On: 5 June 2015 Published On: 22 December 2015

How to Cite: Nagai, I. (2015). Optimization of Penalty Parameter in Penalized Nonlinear Canonical Correlation Analysis by using Cross-Validation. Journal of Mathematics and Statistics, 11(3), 99-106. https://doi.org/10.3844/jmssp.2015.99.106

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Keywords

  • Canonical Correlation Analysis
  • Cross-Validation
  • Nonlinear Relationship
  • Penalized Method