Estimating the principal components of correlation matrices from all their empirical eigenvectors
| Autor: | Dario Villamaina, Rémi Monasson |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
education.field_of_study
Covariance matrix Population General Physics and Astronomy Sample (statistics) Condensed Matter - Disordered Systems and Neural Networks 01 natural sciences 010104 statistics & probability Encoding (memory) 0103 physical sciences Principal component analysis Applied mathematics 0101 mathematics 010306 general physics education Random matrix Eigenvalues and eigenvectors Hamiltonian (control theory) Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | 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. Comment: 6 pages, 6 figures, to appear in Europhysics Letters |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|