A new batch SOM algorithm for relational data with weighted medoids

The great majority of previous works on SOM concern quantitative vectorial data. Nowadays, relatively few SOM algorithms are able to manage relational data despite their usefulness. This paper proposes a new batch SOM algorithm for relational data with weighted medoids. The particularity of the proposed approach is to consider the cluster representatives as vectors of weights whose components measure how objects are weighted as a medoid in a given cluster. From an initial solution and for a fixed epoch and radius, the proposed training batch SOM algorithm provides a partition and cluster representatives by optimizing a suitable objective function aiming to preserve the topological properties of the data on the map. Experiments with datasets of UCI machine learning repository, in comparison with relevant medoid-based batch SOM for relational data algorithms, showed the usefulness of the proposed method.