  Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into
the complex functioning of the human brain, detailing the hemodynamic activity
of thousands of voxels during hundreds of sequential time points. One approach
towards illuminating the connection between fMRI and cognitive function is
through decoding; how do the time series of voxel activities combine to provide
information about internal and external experience? Here we seek models of fMRI
decoding which are balanced between the simplicity of their interpretation and
the effectiveness of their prediction. We use signals from a subject immersed
in virtual reality to compare global and local methods of prediction applying
both linear and nonlinear techniques of dimensionality reduction. We find that
the prediction of complex stimuli is remarkably low-dimensional, saturating
with less than 100 features. In particular, we build effective models based on
the decorrelated components of cognitive activity in the classically-defined
Brodmann areas. For some of the stimuli, the top predictive areas were
surprisingly transparent, including Wernicke's area for verbal instructions,
visual cortex for facial and body features, and visual-temporal regions for
velocity. Direct sensory experience resulted in the most robust predictions,
with the highest correlation ($c \sim 0.8$) between the predicted and
experienced time series of verbal instructions. Techniques based on non-linear
dimensionality reduction (Laplacian eigenmaps) performed similarly. The
interpretability and relative simplicity of our approach provides a conceptual
basis upon which to build more sophisticated techniques for fMRI decoding and
offers a window into cognitive function during dynamic, natural experience.
