We introduce relational variants of neural gas, a very efficient and

powerful neural clustering algorithm. It is assumed that a similarity or

dissimilarity matrix is given which stems from Euclidean distance or dot

product, respectively, however, the underlying embedding of points is unknown.

In this case, one can equivalently formulate batch optimization in

terms of the given similarities or dissimilarities, thus providing a way to

transfer batch optimization to relational data. Interestingly, convergence

is guaranteed even for general symmetric and nonsingular metrics.