A characteristic feature of the vertebrate sensory cortex (and
midbrain) is the existence of multiple two-dimensional map
representations. The authors have constructed a multiple-map
classifier, which permits abstraction of the computational properties
of a multiple-map architecture. They identify three problems which
characterize a multiple-map classifier: classification in two
dimensions, mapping from high dimensions to two dimensions, and
combination of multiple maps. They demonstrate component solutions to
each of the problems, using Parzen-window density estimation in two
dimensions, a generalized Fisher discriminant function for
dimensionality reduction, and split/merge methods to construct a 'tree
of maps' for the multiple-map representation. The combination of
components is modular and each component could be improved or replaced
without affecting the other components. The classifier training
procedure requires time which is linear in the number of training
examples; classification time is independent of the number of training
examples and requires constant space. Performance of this classifier
on Fisher's (1936) iris data, Gaussian clusters on a five-dimensional
simplex, and digitized speech data is comparable to competing
algorithms, such as nearest-neighbor, back-propagation and Gaussian
classifiers. This work provides an example of the computational
utility of multiple-map representation for classification. It is one
step towards the goal of understanding why brain areas such as the
visual cortex utilize multiple map-like representations of the world