The eigenstructure of block-structured correlation matrices and its implications for principal component analysis

Jorge Cadima, Francisco Lage Calheiros and Isabel Preto

Journal of Applied Statistics, 2010, vol. 37, issue 4, 577-589

Abstract: Block-structured correlation matrices are correlation matrices in which the p variables are subdivided into homogeneous groups, with equal correlations for variables within each group, and equal correlations between any given pair of variables from different groups. Block-structured correlation matrices arise as approximations for certain data sets' true correlation matrices. A block structure in a correlation matrix entails a certain number of properties regarding its eigendecomposition and, therefore, a principal component analysis of the underlying data. This paper explores these properties, both from an algebraic and a geometric perspective, and discusses their robustness. Suggestions are also made regarding the choice of variables to be subjected to a principal component analysis, when in the presence of (approximately) block-structured variables.

Keywords: block-structured correlation matrices; eigendecomposition; principal component analysis; within-group eigenpairs; between-group eigenpairs (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1080/02664760902803263

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