  Information mapping is a popular application of Multivoxel Pattern Analysis
(MVPA) to fMRI. Information maps are constructed using the so called
searchlight method, where the spherical multivoxel neighborhood of every voxel
(i.e., a searchlight) in the brain is evaluated for the presence of
task-relevant response patterns. Despite their widespread use, information maps
present several challenges for interpretation. One such challenge has to do
with inferring the size and shape of a multivoxel pattern from its signature on
the information map. To address this issue, we formally examined the geometric
basis of this mapping relationship. Based on geometric considerations, we show
how and why small patterns (i.e., having smaller spatial extents) can produce a
larger signature on the information map as compared to large patterns,
independent of the size of the searchlight radius. Furthermore, we show that
the number of informative searchlights over the brain increase as a function of
searchlight radius, even in the complete absence of any multivariate response
patterns. These properties are unrelated to the statistical capabilities of the
pattern-analysis algorithms used but are obligatory geometric properties
arising from using the searchlight procedure.
