  Functional neuroimaging can measure the brain?s response to an external
stimulus. It is used to perform brain mapping: identifying from these
observations the brain regions involved. This problem can be cast into a linear
supervised learning task where the neuroimaging data are used as predictors for
the stimulus. Brain mapping is then seen as a support recovery problem. On
functional MRI (fMRI) data, this problem is particularly challenging as i) the
number of samples is small due to limited acquisition time and ii) the
variables are strongly correlated. We propose to overcome these difficulties
using sparse regression models over new variables obtained by clustering of the
original variables. The use of randomization techniques, e.g. bootstrap
samples, and clustering of the variables improves the recovery properties of
sparse methods. We demonstrate the benefit of our approach on an extensive
simulation study as well as two fMRI datasets.
