A Note on Topology Preservation in Classification, and the Construction of a Universal Neuron Grid

Abstract

It will be shown that according to theorems of K. Menger, every neuron grid if identified with a curve is able to preserve the adopted qualitative structure of a data space. Furthermore, if this identification is made, the neuron grid structure can always be mapped to a subset of a universal neuron grid which is constructable in three space dimensions. Conclusions will be drawn for established neuron grid types as well as neural fields.