Exploiting the Structures of the U-Matrix

The U-matrix has become a standard visualization of self-organizing feature maps (SOM). Here we present the abstract U-matrix, which formalizes the structures on a U-matrix such that distance calculations between best-matching units w.r.t. the height structures of a U-matrix are precisely defined (U-cell distance). This enables the assessment of the topological correctness of the SOM and the implementation of clustering algorithms that take the structures seen on the U-matrix into account. A weighted Delaunay graph of the U-cell distances allows the calculation of a dendrogram corresponding to the structures of the U-matrix. The method is shown to detect and visualize meaningful cluster structures on difficult artificial and real-life data.