Figure 1. Linearizing encoding and decoding models.
[Top] The brain can be viewed as a system that nonlinearly maps stimuli into brain activity. According to this perspective a central task of systems and cognitive neuroscience is to discover the nonlinear mapping between input and activity. [Middle] Linearizing encoding model. The relationship between encoding and decoding can be described in terms of a series of abstract spaces. In experiments using visual stimuli the axes of the input space are the luminance of pixels and each point in the space (here different colors in the input space) represents a different image. Brain activity measured in each voxel is represented by an activity space. The axes of the activity space correspond to the activity of different voxels and each point in the space represents a unique pattern of activity across voxels (different colors in the activity space). In between the input and activity spaces is a feature space. The mapping between the input space and the feature space is nonlinear and the mapping between the feature space and activity space is linear. [Bottom] Linear classifier. The linear classifier is a simple decoding model that can also be described in terms of input, feature and activity spaces. However, the direction of the mapping between activity and feature space is reversed relative to the encoding model. Because the features are discrete all points in the feature space lie along the axes