Geographic Grid Embeddings

data. Given a map with regions, and some data attributes for each region, we
wish to display this data in a clear and easily readable format. Our approach
represents the map by a regular grid in which spatial relations between the
regions are preserved. We model the mapping between regions and grid cells as a
point set matching problem, and we give various criteria for this matching. We
then focus on one of these criteria: minimising the total distance between the
matched points. Additionally we try to find an optimal translation that
minimises this distance. To this end we characterise optimal translations for
three distance metrics: the Manhattan distance, the Manhattan min-max distance,
and the squared euclidean distance.