文章基本信息

标题：Maximization of Correlation under a Quadratic Constraint
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作者：Akihiro Hashimoto ; Hisao Miyano ; Masaaki Taguri 等
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2007
卷号：37
期号：1
页码：105-121
DOI：10.14490/jjss.37.105
出版社：JAPAN STATISTICAL SOCIETY
摘要：An algebraic method is suggested to search for the optimal solution that maximizes a correlation criterion under a quadratic constraint. First it is shown that the problem formulated in a sample space can be reformulated in a parameter space, and then some properties of a matrix which specifies the quadratic constraint are provided along with its geometrical interpretation; the solution can be obtained by solving a nonlinear equation derived from the singular value decomposition of the matrix. Numerical results based on artificial data and entrance examination data are given to examine how our solution differs from the least squares solution under a quadratic constraint.
关键词：canonical correlation;correlation coefficient;nonlinear optimization;quadratic constraint;singular value decomposition