A "Neural-Gas" Network Learns Topologies

Abstract

A neural network algorithm for vector quantization of topologically arbitrarily struc- tured manifolds of input signals is presented and applied to a. data manifold M which consists of subsets of different dimensionalities. In addition to the quantization of M each neural unit i, i = 1, ... , N of the network A develops connections, described by Cij E 0, 1, to those neural units j with adjacent receptive fields. The resulting con- nectivity matrix Cij describes asymptotically the neighborhood relationships among the input data of the quantized manifold and defines a graph which reflects the often a priori unknown dimensionality and topological structure of the data manifold M.