Measuring topology preservation in maps of real-world data

Topography of neural maps is an advantageous property, e.g. in the presence of noise in a transmission channel or for data visualization. Yet, this property is difficult to define and to quantify. Reviewing some recently proposed measures to quantify topography, we give results for maps trained on synthetic data as well as on four real-world data sets. The measures are found to do not a perfect, but an adequate job, e.g. in selecting a topographically optimal output space dimension.