An alternating variable method for the maximal correlation problem

doi:10.1007/s10898-011-9758-2

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	An alternating variable method for the maximal correlation problem
	Zhang, Lei-Hong 2; Liao, Li-Zhi 1
刊名	JOURNAL OF GLOBAL OPTIMIZATION
	2012-09
卷号	54 期号:1 页码:199-218
关键词	Multivariate statistics Canonical correlation Maximal correlation problem Multivariate eigenvalue problem Power method Gauss-Seidal method Global maximizer
ISSN号	0925-5001
DOI	10.1007/s10898-011-9758-2
英文摘要	The maximal correlation problem (MCP) aiming at optimizing correlations between sets of variables plays an important role in many areas of statistical applications. Up to date, algorithms for the general MCP stop at solutions of the multivariate eigenvalue problem (MEP), which serves only as a necessary condition for the global maxima of the MCP. For statistical applications, the global maximizer is quite desirable. In searching the global solution of the MCP, in this paper, we propose an alternating variable method (AVM), which contains a core engine in seeking a global maximizer. We prove that (i) the algorithm converges globally and monotonically to a solution of the MEP, (ii) any convergent point satisfies a global optimal condition of the MCP, and (iii) whenever the involved matrix A is nonnegative irreducible, it converges globally to the global maximizer. These properties imply that the AVM is an effective approach to obtain a global maximizer of the MCP. Numerical testings are carried out and suggest a superior performance to the others, especially in finding a global solution of the MCP.
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000307289300014
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2115]
专题	上海财经大学
通讯作者	Liao, Li-Zhi
作者单位	1.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China; 2.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei-Hong,Liao, Li-Zhi. An alternating variable method for the maximal correlation problem[J]. JOURNAL OF GLOBAL OPTIMIZATION,2012,54(1):199-218.
APA	Zhang, Lei-Hong,&Liao, Li-Zhi.(2012).An alternating variable method for the maximal correlation problem.JOURNAL OF GLOBAL OPTIMIZATION,54(1),199-218.
MLA	Zhang, Lei-Hong,et al."An alternating variable method for the maximal correlation problem".JOURNAL OF GLOBAL OPTIMIZATION 54.1(2012):199-218.