Ontology type: schema:Chapter Open Access: True
2013
AUTHORSClaire Caillerie , Frédéric Chazal , Jérôme Dedecker , Bertrand Michel
ABSTRACTThis 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... »
PAGES561-568
Geometric Science of Information
ISBN
978-3-642-40019-3
978-3-642-40020-9
http://scigraph.springernature.com/pub.10.1007/978-3-642-40020-9_62
DOIhttp://dx.doi.org/10.1007/978-3-642-40020-9_62
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