M (2007) Topographic processing of relational data

Abstract Recently, batch optimization schemes of the self-organizing map (SOM) and neural gas (NG) have been modied to so-called median variants which allow a transfer of these methods to arbitrary distance measures be-yond the standard euclidean metric. This principle is par-ticularly suitable for complex applications where data are compared by means of problem-specic, possibly discrete metrics such as protein sequences which are compared by FASTA or BLAST. However, median variants do not allow a continuous update of prototype locations and their capac-ity is thus restricted in particular for small data sets. 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 distance matri-ces without known euclidean embedding becomes possi-ble. 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. These algorithms are evaluated in several experiments.