Strain-minimizing hyperbolic network embeddings with landmarks

Abstract We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into space, which requires only the measurements to few ‘landmark nodes’. This landmark heuristic makes applicable large-scale graphs improves upon previously introduced methods. As mathematical justification, we show that point configuration in $d$-dimensional space can be perfectly recovered (up isometry) from just $d+1$ landmarks. also solves two-stage strain-minimization problem, similar our previous (unlandmarked) ‘hydra’. Testing on real network data, is an order of magnitude faster than existing methods scales linearly number nodes. While error higher methods, extension, L-hydra+, outperforms both runtime quality.