Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models
Fig 9
Stability of modes of shared variability in network models.
(A) Principal angles between top five modes in clustered network for 20- (blue), 40- (black), or 80-neuron (red) analyses and corresponding neurons from 500-neuron analyses. Modes were identified by computing the eigenvectors of the shared covariances corresponding to neurons from the 20-neuron set. Plots show mean and standard error across 25 sets of 500 neurons and 10,000 trials. Grey circles represent principal angles (mean ± one standard deviation) between random 20-dimensional vectors. (B) Principal angles between modes in the non-clustered network. Same conventions as in (A). (C) Percent shared variance along each mode in the clustered network for 80-neuron analyses (red) and 500-neuron analyses (black) shown in (A). The maximum number of modes across the 25 sets was 75 for the 80-neuron analysis and 130 for the 500-neuron analysis. The two curves were nearly identical between modes 50 and 75 and therefore only the first 100 modes are shown. Curves represent mean percent shared variance for each mode across 25 sets. Error bars show standard error computed across the 25 sets. (D) Percent shared variance along each mode in the non-clustered network for the 80-neuron analyses (red) and the 500-neuron analyses (black) used in (B). Same conventions as in (C). The maximum number of modes across the 25 sets was 45 in the 80-neuron analysis and 130 for the 500-neuron analysis. Inset shows zoomed in vertical axis.