Information integration in large brain networks
Fig 2
We first tested our spectral clustering-based approach in small simulations.
A This is an example of a small brain-like network we generated using a novel algorithm based on Hebbian plasticity. This algorithm produces networks that are loosely brain-like, in that they are modular, show rich cross-module connectivity, and display a log-normal degree distribution with long right tails. We used this algorithm to generate 50 14- and 16-node networks. see Methods for more details on network generation. B This is a sample of oscillatory data generated from the network in A. We generated these data using a stochastic coupled Rössler oscillator model. In the Rössler oscillator model, each node stochastically oscillates according to its own intrinsic frequency, and dynamically synchronizes with other nodes it is connected to. The resulting data are multivariate normal (S2 Fig), allowing for the fast computation of integrated information. C As a first test of our spectral clustering-based approach to identifying the MIB from time-series data, we subtracted ΦG (normalized) across the ground-truth MIB, identified through a brute-force search through all possible bipartitions, from ΦG (normalized) across the partitions identified through spectral clustering. In this test, a perfect match between values would yield a difference of 0 bits. Red squares indicate the mean across 50 networks, and the blue bars indicate standard error of the mean. D As a second test of our spectral clustering-based approach, we computed the Rand Index [45], which is a common measure of partition similarity, between the spectral partitions and the ground-truth MIBs of these networks. A Rand Index of 1 indicates a perfect match between partitions, and a Rand Index of 0 indicates maximum dissimilarity between partitions. Red squares indicate the mean across 50 networks, and the blue bars indicate standard error of the mean. These results show that spectral clustering finds the MIB of small networks of coupled oscillators. We found similar results using the same networks but with autoregressive network dynamics (S7 Fig).