Exploiting data topology in visualization and clustering of self-organizing maps

The self-organizing map (SOM) is a powerful method for visualization, cluster extraction, and data mining. It has been used successfully for data of high dimensionality and complexity where traditional methods may often be insufficient. In order to analyze data structure and capture cluster boundaries from the SOM, one common approach is to represent the SOM's knowledge by visualization methods. Different aspects of the information learned by the SOM are presented by existing methods, but data topology, which is present in the SOM's knowledge, is greatly underutilized. We show in this paper that data topology can be integrated into the visualization of the SOM and thereby provide a more elaborate view of the cluster structure than existing schemes. We achieve this by introducing a weighted Delaunay triangulation (a connectivity matrix) and draping it over the SOM. This new visualization, CONNvis, also shows both forward and backward topology violations along with the severity of forward ones, which indicate the quality of the SOM learning and the data complexity. CONNvis greatly assists in detailed identification of cluster boundaries. We demonstrate the capabilities on synthetic data sets and on a real 8-D remote sensing spectral image.