

Abstract:
Many realworld data sets can be viewed of as noisy samples of special types of metric spaces called metric graphs. Building on the notions of correspondence and GromovHausdorff distance in metric geometry, we describe a model for such data sets as an approximation of an underlying metric graph. We present a novel algorithm that takes as an input such a data set, and outputs a metric graph that is homeomorphic to the underlying metric graph and has bounded distortion of distances. We also implement the algorithm, and evaluate its performance on a variety of real world data sets.
