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A graphical procedure for comparing the principal components of several covariance matrices

 

作者: E. M. Keramidas,   S. J Devlin,   R Gnanadesikan,  

 

期刊: Communications in Statistics - Simulation and Computation  (Taylor Available online 1987)
卷期: Volume 16, issue 1  

页码: 161-191

 

ISSN:0361-0918

 

年代: 1987

 

DOI:10.1080/03610918708812583

 

出版商: Marcel Dekker, Inc.

 

关键词: eigenvectors;dispersion matrices;direction of scatters;orientation of point clouds

 

数据来源: Taylor

 

摘要:

Principal components analysis is an extensively used tool for reduction of dimensionality in multivariate analyses. In many applications, however, little attempt is made to compare principal components solutions (i.e., eigenvectors) across many samples. Methods are needed for assessing the degree of similarity of corresponding eigenvectors, a problem that is meaningful in the presence of clearly separated eigenvalues. This paper proposes a gamma probability plotting procedure for a measure of the angle between a pair of eigenvectors, or equivalently, the distance between points on the unit sphere defined by such vectors. One of the vectors in the pair is the principal component of a sample and the other can be either a prespecified vector or a “typical” vector obtained from the corresponding eigenvectors in all samples. Simulations, as well as real-data examples, are presented

 

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