  An outstanding problem in neuroscience is to understand how information is
integrated across the many modules of the brain. While classic
information-theoretic measures have transformed our understanding of
feedforward information processing in the brain's sensory periphery, comparable
measures for information flow in the massively recurrent networks of the rest
of the brain have been lacking. To address this, recent work in information
theory has produced a sound measure of network-wide "integrated information,"
which can be estimated from time-series data. But, a computational hurdle has
stymied attempts to measure large-scale information integration in real brains.
Specifically, the measurement of integrated information involves a
combinatorial search for the informational "weakest link" of a network, a
process whose computation time explodes super-exponentially with network size.
Here, we show that spectral clustering, applied on the correlation matrix of
time-series data, provides an approximate but robust solution to the search for
the the informational weakest link of large networks. This reduces the
computation time for integrated information in large systems from longer than
the lifespan of the universe to just minutes. We evaluate this solution in
brain-like systems of coupled oscillators as well as in high-density
electrocortigraphy data from two macaque monkeys, and show that the
informational "weakest link" of the monkey cortex splits posterior sensory
areas from anterior association areas. Finally, we use our solution to provide
evidence in support of the long-standing hypothesis that information
integration is maximized by networks with a high global efficiency, and that
modular network structures promote the segregation of information.
