Assessing dot-map aggregations

Compositional geospatial data can be visualized as dot maps, where the color of each dot represents its class. For interactive dots maps, where it is possible to zoom out in order to see the global picture, it is often needed to aggregate the dots. Hence, we face the following aggregation problem: let M be an input matrix where each cell is assigned a class; find an aggregated matrix A in which each cell aligns with k by k cells of M such that A is a good summary of M.We distinguish three dimensions of “good summary”: class balance, representation and presence. The first is holistic, whereas the othertwo capture spatial aspects. We propose a simple heuristic algorith