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Riemannian Trust-Region Method for the Maximal Correlation Problem

机译:极大相关问题的黎曼信赖域方法

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The maximal correlation problem (MCP) arising in the canonical correlation analysis is very important to assess the relationship between sets of random variables. Efficient and fast methods for solving MCP are desired in broad statistical and nonstatistical applications. Some early proposed algorithms are based on the first-order information of MCP, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust-region method of Absil et al. [22. P.-A. Absil , C. G. Baker , and K. A. Gallivan ( 2007 ). Trust-region methods on Riemannian manifolds . Found. Comput. Math. 7 : 303 - 330 .View all references] into a practical algorithm for MCP, which enjoys the global convergence and local superlinear convergence rate. The structure-exploiting preconditioning technique is also discussed in solving the trust-region subproblem. Numerical empirical evaluation and a comparison against other methods are reported, which shows that the method is efficient in solving MCPs.View full textDownload full textKeywordsCanonical correlation analysis, Global convergence, Multivariate statistics, Precondition, Riemannian trust-region method, Superlinear convergence2000 Mathematics Subject Classification62H20, 15A12, 65F10, 65K05Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/01630563.2011.618961
机译:典范相关分析中出现的最大相关问题(MCP)对于评估随机变量集之间的关系非常重要。在广泛的统计和非统计应用中,需要一种有效且快速的方法来解决MCP。一些较早提出的算法是基于MCP的一阶信息,因此无法期望快速收敛。在本文中,我们将转向Absil等人的通用黎曼信赖域方法。 [22。 P.-A. Absil,C.G.Baker和K.A.Gallivan(2007)。黎曼流形上的信赖域方法。找到了。计算数学。 7:303-330 [查看所有参考资料]成为一种适用于MCP的实用算法,该算法享有全局收敛性和局部超线性收敛率。在解决信任区域子问题中,还讨论了利用结构的预处理技术。进行了数值经验评估并与其他方法进行了比较,表明该方法可有效解决MCP问题。查看全文下载全文关键词典型相关分析,全局收敛,多元统计,前提,黎曼信赖域方法,超线性收敛2000数学主题分类62 ,15A12、65F10、65K05相关var addthis_config = {ui_cobrand:“泰勒和弗朗西斯在线”,servicescompact:“ citlikelike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,更多”,pubid:“ ra- 4dff56cd6bb1830b“};添加到候选列表链接永久链接http://dx.doi.org/10.1080/01630563.2011.618961

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