VRGrid: Efficient Transformation of 2D Data into Pixel Grid Layout

Projecting a set of
$n$
points on a grid of size
$\sqrt{n}\times\sqrt{n}$
provides the best possible information density in two dimensions without overlap. We leverage the Voronoi Relaxation method to devise a novel and versatile post-processing algorithm called VRGrid: it enables the arrangement of any 2D data on a grid while preserving its initial positions. We apply VRGrid to generate compact and overlap-free visualization of popular and overlap-prone projection methods (e.g., t-SNE). We prove that our method complexity is
$O(\sqrt{n}.i.n.log(n))$
, with i a determined maximum number of iterations and
$n$
the input dataset size. It is thus usable for visualization of several thousands of points. We evaluate VRGrid's efficiency with several metrics: distance preservation (DP), neighborhood preservation (NP), pairwise relative positioning preservation (RPP) and global positioning preservation (GPP). We benchmark VRGrid against two state-of-the-art methods: Self-Sorting Maps (SSM) and Distance-preserving Grid (DGrid). VRGrid outperforms these two methods, given enough iterations, on DP, RPP and GPP which we identify to be the key metrics to preserve the positions of the original set of points.