In many real world applications, data cannot be accurately represented by
vectors. In those situations, one possible solution is to rely on dissimilarity
measures that enable sensible comparison between observations. Kohonen's
Self-Organizing Map (SOM) has been adapted to data described only through their
dissimilarity matrix. This algorithm provides both non linear projection and
clustering of non vector data. Unfortunately, the algorithm suffers from a high
cost that makes it quite difficult to use with voluminous data sets. In this
paper, we propose a new algorithm that provides an important reduction of the
theoretical cost of the dissimilarity SOM without changing its outcome (the
results are exactly the same as the ones obtained with the original algorithm).
Moreover, we introduce implementation methods that result in very short running
times. Improvements deduced from the theoretical cost model are validated on
simulated and real world data (a word list clustering problem). We also
demonstrate that the proposed implementation methods reduce by a factor up to 3
the running time of the fast algorithm over a standard implementation