Estimating the principal components of correlation matrices from all their empirical eigenvectors

Abstract

We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the eigenmodes of the sample correlation matrices are informative, and not only the top ones. We show how this information can be exploited when prior information about the principal component, such as whether it is localized or not, is available by mapping the estimation problem onto the search for the ground state of a spin-glass-like effective Hamiltonian encoding the prior. Results are illustrated numerically on the spiked covariance model.

6 pages, 6 figures, to appear in Europhysics Letters

References in corpus (4)

• Large Deviations of Extreme Eigenvalues of Random Matrices
• Finite sample approximation results for principal component analysis: a matrix perturbation approach
• Eigenvector dynamics: general theory and some applications
• Sampling eigenmodes in colloidal solids

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