Metric graph reconstruction from noisy data

Authors:
Mridul Aanjaneya;Frederic Chazal;Daniel Chen;Marc Glisse;Leonidas J. Guibas;Dmitriy Morozov
Affiliations:
Stanford University, Stanford, CA, USA;INRIA Saclay , Orsay, France;Stanford University, Stanford, CA, USA;INRIA Saclay , Orsay, France;Stanford University, Stanford, CA, USA;Stanford University, Stanford, CA, USA
Venue:
Proceedings of the twenty-seventh annual symposium on Computational geometry
Year:
2011

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Abstract

Many real-world data sets can be viewed of as noisy samples of special types of metric spaces called metric graphs [16]. Building on the notions of correspondence and Gromov-Hausdorff 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 the underlying metric graph with guarantees. We also implement the algorithm, and evaluate its performance on a variety of real world data sets.