Table 2.

Effect of different response-pattern normalizations

Geometric intuition for...	Normalization type	Subtract mean	Subtract mean and divide by s.d.
Response response pattern for each stimulus	(1) across stimuli	Pattern shape changed.	Pattern shape changed: Voxels of high variance across stimuli are downscaled.
	(2) across voxels	Pattern shape preserved, but mean-level shifted: spatial- mean response is 0 for all stimuli.	Pattern shape preserved, but shifted and scaled: spatial- mean response and variability across voxels is equal for all stimuli.
Sample sample distribution in voxels’ response space	(1) across stimuli	Distribution is centered on the origin in each dimension.Distribution is shifted in each dimension.	Distribution is centered on the origin and scaled to unit standard-deviation in each dimension.Distribution is shifted and scaled in each dimension.
	(2) across voxels	Distribution is shrunkprojected onto thea hyperplane: tThe dimensionality of the sample distribution is reduced by 1 as samples are projected onto the hyperplane orthogonal to the all-1 vector.	Distribution is shrunkprojected onto thea hypersphere within the hyperplane: tThe dimensionality of the sample distribution is reduced by 2 as samples are projected onto a centered hypersphere within the hyperplane.