Improved Interpretability of the Unified Distance Matrix with Connected Components

Self-organizing maps have been adopted in many fields as the data visualization method of choice. The unified distance matrix is the de facto standard for evaluating and interpreting self-organizing maps. In large, high-dimensional problems clusters can be difficult to identify in the plain unified distance matrix. Here we introduce an enhanced version of the unified distance matrix in which clusters are easier to see and interpret. In this enhanced version we view the self-organizing map as a planar graph where the clusters are connected components of this graph. Using the transitive properties of connectedness and exploiting the fact that each component has a minimal node where the gradient on the unified distance matrix is equal to zero we can transform these connected components into stars with the minimal node as the internal node. In order to avoid unnecessary fragmentation of the components we apply a kernel based smoothing algorithm to the unified distance matrix. Our enhanced unified distance matrix is then the smoothed original unified distance matrix with the star components overlaid. The result is an easily interpretable selforganizing map. We perform a number of experiments on synthetic as well as real-world data that highlight the increased visual power of this enhanced unified distance matrix. Fig. 1. A unified distance matrix.