Figure 1.

Dimensionality of population-wide fluctuations. (a) Responses of two simulated neural populations with low-dimensional (upper row) and high-dimensional (lower row) fluctuations on four example trials (different trials are offset vertically). Blue-to-green color code indicates projection of each trial on the first principal component (see Box 1) of the data correlation matrix. Neurons are sorted left-to-right by their activity on the first trial (blue). Across trials, low-dimensional population exhibits only a scaled version of the same activity pattern. High-dimensional population exhibits many diverse activity patterns. (b) Noise correlation (see Box 1) is a Pearson correlation coefficient between activities of a pair of neurons (i and j) in the population across trials, under identical stimulus conditions (each dot is the pair’s activity on one trial). (c) Noise correlation matrix for all pairs in the population. Neurons are sorted according to their projection weight on the first principal component. (d) Eigenvalue spectrum of the noise-correlation matrix decays slowly for the high-dimensional population, but has only one eigenvalue set apart from zero for the low-dimensional population (see Box 1).