NeuroScale: Novel Topographic Feature Extraction using RBF Networks

Further details may be found in (Lowe, 1993; Lowe and Tipping, 1996). We seek a dimension-reducing, topographic transformation of data for the purposes of visualisation and analysis. By'topographic', we imply that the geometric structure of the data be optimally preserved in the transformation, and the embodiment of this constraint is that the inter-point distances in the feature space should correspond as closely as possible to those distances in the data space. The implementation of this principle by a neural network is very simple. A Radial Basis Function (RBF) neural network is utilised to predict the coordinates of the data point in the transformed feature space. The locations of the feature points are indirectly determined by adjusting the weights of the network. The transformation is determined by optimising the network parameters in order to minimise a suitable error measure that embodies the topographic principle. The specific details of this alternative approach are as follows.