Computing absolute maximum correlation

doi:10.1093/imanum/drq029

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	Computing absolute maximum correlation
	Zhang, Lei-Hong 1; Chu, Moody T.2
刊名	IMA JOURNAL OF NUMERICAL ANALYSIS
	2012-01
卷号	32 期号:1 页码:163-184
关键词	multivariate statistics canonical correlation multivariate eigenvalue problem power method Gauss-Seidal method global maximizer
ISSN号	0272-4979
DOI	10.1093/imanum/drq029
英文摘要	Optimizing correlations between sets of variables is an important task in many areas of applications. There are plenty of algorithms for computing the maximum correlation. Most disappointingly, however, is that these methods typically cannot guarantee attaining the absolute maximum correlation, which would have significant impact on practical applications. This paper makes two contributions. Firstly, some distinctive traits of the absolute maximum correlation are characterized. By exploiting these attributes it is possible to propose an effective starting-point strategy that significantly increases the likelihood of attaining the absolute maximum correlation. Numerical testing of the classical Horst algorithm with the starting-point strategy seems to evince the potency of this approach. Secondly, the Horst algorithm is but one aggregated Jacobi-type power method. Following the innate iterative structure, a generalization to the Gauss-Seidel formulation is proposed as a natural improvement on the power method. Monotone convergence of the Gauss-Seidel algorithm is proved. When combined with the starting-point strategy, the newer Gauss-Seidel approach leads to faster computation of the absolute maximum correlation.
WOS研究方向	Mathematics
语种	英语
出版者	OXFORD UNIV PRESS
WOS记录号	WOS:000299350400007
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2202]
专题	上海财经大学
通讯作者	Zhang, Lei-Hong
作者单位	1.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China; 2.N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
推荐引用方式 GB/T 7714	Zhang, Lei-Hong,Chu, Moody T.. Computing absolute maximum correlation[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2012,32(1):163-184.
APA	Zhang, Lei-Hong,&Chu, Moody T..(2012).Computing absolute maximum correlation.IMA JOURNAL OF NUMERICAL ANALYSIS,32(1),163-184.
MLA	Zhang, Lei-Hong,et al."Computing absolute maximum correlation".IMA JOURNAL OF NUMERICAL ANALYSIS 32.1(2012):163-184.