Fundamental Limitations of Inverse Projections and Decision Maps

Inverse projection techniques and decision maps are recent tools proposed to depict the behavior of a classifier using 2D visualizations. However, which parts of the large, high-dimensional, space such techniques actually visualize, is still unknown. A recent result hinted at the fact that such techniques only depict a two-dimensional manifold from the entire data space. In this paper, we investigate the behavior of inverse projections and decision maps in high dimensions with the help of intrinsic dimensionality estimation methods. We find that the inverse projections are always surface-like no matter what decision map method is used and no matter how high the data dimensionality is, i.e., the intrinsic dimensionality of inverse projections is always two. Thus, decision boundaries displayed by decision maps are the intersection of the backprojected surface and the actual decision surfaces. Our finding reveals a fundamental problem of all existing decision map techniques in constructing an effective visualization of the decision space. Based on our findings, we propose solutions for future work in decision maps to address this problem.