Monitoring the formation of kernel-based topographic maps

Topographic maps have attracted the attention of the data mining community since they can be used for representing and visualizing multidimensional data. For applications like these, it is crucial that the maps are free of topological defects. We introduce a new algorithm for monitoring the degree of topology preservation of kernel-based maps during learning. The algorithm is applied to a synthetic example in this article, and a large, real-world example in our companion article.