Dimensionality-reduction using connectionist networks

A method is presented for using connectionist networks of simple computing elements to discover a particular type of constraint in multidimensional data. Suppose that some data source provides samples consisting of n-dimensional feature-vectors, but that this data all happens to lie on an m-dimensional surface embedded in the n-dimensional feature space. Then occurrences of data can be more concisely described by specifying an m-dimensional location of the embedded surface than by reciting all n components of the feature vector. The recording of data in such a way is known as dimensionality-reduction. A method is presented for performing dimensionality-reduction in a wide class of situations for which an assumption of linearity need not be made about the underlying constraint surface. The method takes advantage of self-organizing properties of connectionist networks of simple computing elements. The authors present a scheme for representing the values of continuous (scalar) variables in subsets of units.>