Topology preservation in SOFM: An euclidean versus manhattan distance comparison

Abstract

The Self-Organising Feature Map (SOFM) is one of the unsupervised neural models of most widespread use. Several studies have been carried out in order to determine the degree of topology-preservation for this data projection method, and the influence of the distance measure used, usually Euclidean or Manhattan distance. In this paper, by using a new topologypreserving representation of the SOFM and the well-known Sammon's stress, graphical and numerical comparisons are shown between both possibilities for the distance measure. Our projection method, based on the relative distances between neighbouring neurons, gives similar information to those of the Sammon projection, but in a graphical way.