Topographic Processing of Relational Data

Abstract

Recently, batch optimization schemes of the self-organizing map and neural gas have been modified to allow arbitrary distance measures.This principle is particularly suitable for complex applications where data are compared by means of problem-specific, possibly discrete metrics such as protein sequences. However, median variants do not allow a continuous update of prototype locations and their capacity is thus restricted. In this contribution, we consider the relational dual of batch optimization which can be formulated in terms of pairwise distances only such that an application to arbitrary distance matrices becomes possible. For SOM, a direct visualization of data is given by means of the underlying (euclidean or hyperbolic) lattice structure. For NG, pairwise distances of prototypes can be computed based on a given data matrix only, such that subsequent mapping by means of multidimensional scaling can be applied.