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Spike Triggered Covariance in Strongly Correlated Gaussian Stimuli

Figure 2

Spectra of the population covariance, sample covariance, and symmetric random matrices with matched element distribution.

(A) Eigenvalue distribution of an example population covariance matrix () computed from the van Hateren data set. The largest eigenvalue (marked with an arrow) corresponds to an eigenvector with only positive components, and is times larger than the second largest eigenvalue (also marked) and times larger than the mean eigenvalue. (B) Eigenvalue distribution of a collection of sample covariance matrices computed from stimuli randomly drawn from a multivariate Gaussian distribution . In gray is the analytic prediction for the outstanding eigenvalue. The spread of these eigenvalues (black, inset) is in agreement with the prediction in Eq. (8). (C) Eigenvalue distribution of symmetric random matrices with elements randomly drawn from a distribution given by the elements in the sample covariance matrices. In gray is the complete prediction (semicircle and outstanding eigenvalue) given by Eq. (5). Diagonal and off-diagonal elements are drawn separately from the distribution of matrix elements in panel B.

doi: https://doi.org/10.1371/journal.pcbi.1003206.g002