Cartogram representation of the batch-SOM magnification factor

Model interpretability is a problem of knowledge extraction from the patterns found in raw data. One key source of knowledge is information visualization, which can help us to gain insights into a problem through graphical representations and metaphors. Nonlinear dimensionality reduction techniques can provide flexible visual insight, but the locally varying representation distortion they produce makes interpretation far from intuitive. In this paper, we define a cartogram method, based on techniques of geographic representation, that allows reintroducing this distortion, measured as a magnification factor, in the visual maps of the batch-SOM model. It does so while preserving the topological continuity of the representation.