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

Journal of Mathematics and Statistics

Isamu Nagai¹ 

关键词: Canonical Correlation Analysis;    Cross-Validation;    Nonlinear Relationship;    Penalized Method;   

DOI  :  10.3844/jmssp.2015.99.106

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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

【 授权许可】

Unknown