Metric graph reconstruction from noisy data

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 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 the underlying metric graph with guarantees. We also implement the algorithm, and evaluate its performance on a variety of real world data sets. Categories and Subject Descriptors I.5.1 [Pattern Recognition]: Models—geometric; F.2.2 [Nonnumerical Algorithms and Problems]: [geometrical problems and computations] General Terms Algorithms, Experimentation Keywords Reconstruction, metric graph, noise, inference

• Type: Journal
• Year: 2011
• Where: COMPGEOM
• Authors: Mridul Aanjaneya, Frédéric Chazal, Daniel Chen, Marc Glisse, Leonidas J. Guibas, Dmitriy Morozov
• Keywords: COMPGEOM 2011, Discrete Geometry, Geometrical Problems, Noisy Samples, Recognition Models