Preserving proximity relations and minimizing edge-crossings in high dimensional graph visualizations

We propose a novel approach to drawing graphs that simultaneously optimizes two criteria (i) preserving proximity relations as measured by some embedding objective, and (ii) minimizing edge-crossings, to create a clear representation of the underlying graph structure. Frequently, the nodes of the graph represent objects that have their own intrinsic properties with associated distances or similarity measures. In particular, we investigate graphing of spoligoforests to visualize the genetic relatedness between strains of the Mycobacterium tuberculosis complex using multiple genetic markers. It is often desirable, that drawings of such graphs map nodes from high-dimensional feature space to low-dimensional vectors that preserve these pairwise distances. This desired quality is frequently expressed as a function of the embedding and then optimized, eg. Multidimensional Scaling (MDS), the goal is to minimize the difference between the actual distances and Euclidean distances between all nodes in the embedding.