New method for measuring the topology preservation of self-organizing feature maps

The topology preservation of self-organizing feature maps is an important property which is used in many applications. Various qualitative and quantitative approaches are known for measuring the degree of topology preservation. However, well-received measures for determining the topology preservation have not been presented yet. In this paper, we present a new method for measuring the degree of topology preservation based on the masked Delaunay triangulation. The topology preservation is completed when the masked Delaunay triangulation coincides with the output network shape. We demonstrate the usefulness of this measure for various examples of data manifolds. This method is also applied to measure the degree of topology preservation of the topology-representing network of T. Martinetz et al. (1994). In various simulations, this measure brought a reasonable degree of topology preservation.