Controlling the scatterplot shapes of 2D and 3D multidimensional projections

Multidimensional projections are effective techniques for depicting high-dimensional data. The point patterns created by such techniques, or a technique's visual signature, depend — apart from the data themselves — on the technique design and its parameter settings. Controlling such visual signatures — something that only few projections allow — can bring additional freedom for generating insightful depictions of the data. We present a novel projection technique — ShaRP — that allows explicit control on such visual signatures in terms of shapes of similar-value point clusters (settable to rectangles, triangles, ellipses, and convex polygons) and the projection space (2D or 3D Euclidean or S²). We show that ShaRP scales computationally well with dimensionality and dataset size, provides its signature-control by a small set of parameters, allows trading off projection quality to signature enforcement, and can be used to generate decision maps to explore the behavior of trained machine-learning classifiers.