a, Scatterplots illustrating the noise levels of each estimated PC. Each plot shows population activity projected onto the specified PC, for the first repeat (x axis) and second repeat (y axis). Each point represents responses to a single stimulus. b, Estimated level of noise variance in successive signal dimensions. Noise variance was estimated by subtracting the cvPCA estimate of signal variance from the total variance (see Methods). c, Recovery of ground-truth eigenspectrum in simulated data. We simulated responses of 10,000 neurons to 2,800 stimuli with a power spectrum decay of exactly α = 1, and added noise in the stimulus space, generated with the spectrum in b scaled to produce the same signal-to-noise ratio as in the original neural data. The ground-truth eigenspectrum (black) is estimated accurately by the cvPCA method (blue). d, Same analysis as in c with multiplicative noise, in which the responses of all neurons on each trial were multiplied by a common random factor. The distribution of this factor was again scaled to recover the original signal-to-noise ratio. e, Same analysis as in c with a combination of multiplicative and additive noise. f, Same analysis as in c, also including simulation of neural and two-photon shot noise before running a GCaMP deconvolution algorithm. g, Ten instantiations of the simulation were performed with ground-truth exponents of 0.5, 1.0 and 1.5. Error bars represent standard deviations of the power-law exponents estimated for each of the ten simulations. The dashed black line represents the ground-truth value. h–j, Comparison of cvPCA (yellow) and traditional PCA (green) algorithms in the presence of the additive + multiplicative noise combination. Whereas cvPCA recovered the ground-truth eigenspectrum (black) exactly, traditional PCA did not, resulting in overestimation of the top eigenvalues and failure to detect the ground-truth power law.