A topographic map is an n-dimensional
representation of input vector
s where closeness in the map indicates similarity between inputs.
Such a map is created by the Kohonen neural network. Patterns are presented to the inputs of the network and the most strongly responding unit is updated to respond strongly in future. The neighbours of this unit are also updated to respond strongly, thus similar patterns will make neighbouring units respond strongly.
If a particular feature occurs more frequently in the set of input patterns, more space is allocated in the map to respond to those patterns (i.e. more units respond to patterns with that feature). This allows a higher resolution of identification for those patterns which only differ by a small amount.
A biological example of this is found in the auditory cortex. A tonotopic map is created where neighbouring neurons respond to neighbouring frequencies. Animals that rely on certain frequencies of sound more than others (i.e. a bat uses ultrasound for navigation) will have more neurons allocated to respond to that frequency.