Deconvolution for the Wasserstein Metric and Geometric Inference View Full Text


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Chapter Info

DATE

2013

AUTHORS

Claire Caillerie , Frédéric Chazal , Jérôme Dedecker , Bertrand Michel

ABSTRACT

This paper is a short presentation of recent results about Wasserstein deconvolution for topological inference published in [1]. A distance function to measures has been defined in [2] to answer geometric inference problems in a probabilistic setting. According to their result, the topological properties of a shape can be recovered by using the distance to a known measure ν, if ν is close enough to a measure μ for he Wasserstein distance W 2. Given a point cloud, a natural candidate for ν is the empirical measure μ n . Nevertheless, in many situations the data points are not located on the geometric shape but in the neighborhood of it, and μ n can be too far from μ. In a deconvolution framework, we consider a slight modification of the classical kernel deconvolution estimator, and we give a consistency result and rates of convergence for this estimator. Some simulated experiments illustrate the deconvolution method and its application to geometric inference on various shapes and with various noise distributions. More... »

PAGES

561-568

References to SciGraph publications

  • 2009-04. A Sampling Theory for Compact Sets in Euclidean Space in DISCRETE & COMPUTATIONAL GEOMETRY
  • 2011-12. Geometric Inference for Probability Measures in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 2009. Optimal Transport, Old and New in NONE
  • Book

    TITLE

    Geometric Science of Information

    ISBN

    978-3-642-40019-3
    978-3-642-40020-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-40020-9_62

    DOI

    http://dx.doi.org/10.1007/978-3-642-40020-9_62

    DIMENSIONS

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