Relational Topographic Maps

We introduce relational variants of neural topographic maps including the self-organizing map and neural gas, which allow clustering and visualization of data given as pairwise similarities or dissimilarities with continuous prototype updates. It is assumed that the (dis-)similarity matrix originates from Euclidean distances, however, the underlying embedding of points is unknown.Batch optimization schemes for topographic map formations are formulated in terms of the given (dis-)similarities and convergence is guaranteed, thus providing a way to transfer batch optimization to relational data.