The Principal Component Structure of Natural Sound

Redundancy reduction on the basis of the second-order statistics of natural images has been very successful in accounting for the psychophysics of low-level vision. Here we study the second-order statistics of natural sound ensembles using Principal Component Analysis (PCA). Their eigen spectra exhibit a nite-size scaling behavior as a function of the window size, with universality after the 2{5 milliseconds range. In contrast with natural scenes, auditory spectra do not universally obey a power law, but rather depend strongly on the auditory environment. We study the distribution of the PCA coeecients and nd them highly non-Gaussian, with kurtoses in the mid hundreds. The dependence of the kurto-sis on the eigenmode's average power is non-trivial|highly erratic. Moreover, the kurtosis increases with the size of the window up to, at least, 80 milliseconds, and also becomes more erratic as a function of the eigenmode's power. We compare these results with the ones based on Fourier Analysis, and also discuss their implications for eecient coding of natural auditory stimuli.