DECODING SECOND ORDER ISOMORPHISMS IN THE BRAIN: The case of colors and letters.

We introduce a new method for decoding neural data from fMRI. It is based on two assumptions, first that neural representation is distributed over networks of neurons embeded in voxel noise and second that the stimuli can be decoded as learned relations from sets of categorical stimuli. We illustrate these principles with two types of stimuli, color (wavelength) and letters (visual shape), both of which have early visual system response, but at the same time must be learned within a given function or category (color contrast, alphabet). Key to the decoding method is reducing the stimulus cross-correlation by a matched noise voxel sample by normalizing the stimulus voxel matrix thus unmasking a highly discriminative neural profile per stimulus. Projection of this new voxel space (ROI) to a smaller set of dimensions (with e.g., non-metric Multidimensional scaling), the relational information takes a unique geometric form revealing functional relationships between sets of stimuli, defined by R. Shepard, as second-order isomorphisms (SOI). In the case of colors the SOI appears as a nearly equally spaced set of wavelengths arranged in a color wheel, with a gap between the "purples" and "reds" (consistent with the gap in the original Ekmans color set). In the case of letters, a cluster space resulted from the decorrelated voxel neural profiles, which matched the phrase structure of the mnemonic used for more than 100 years to teach children the alphabet (across multiple languages), The Alphabet Song.