License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SOCG.2015.827
URN: urn:nbn:de:0030-drops-51052
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5105/
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Buchet, Mickaël ; Chazal, Frédéric ; Dey, Tamal K. ; Fan, Fengtao ; Oudot, Steve Y. ; Wang, Yusu

Topological Analysis of Scalar Fields with Outliers

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Abstract

Given a real-valued function f defined over a manifold M embedded in R^d, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice.

We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field.

BibTeX - Entry

@InProceedings{buchet_et_al:LIPIcs:2015:5105,
  author =	{Micka{\"e}l Buchet and Fr{\'e}d{\'e}ric Chazal and Tamal K. Dey and Fengtao Fan and Steve Y. Oudot and Yusu Wang},
  title =	{{Topological Analysis of Scalar Fields with Outliers}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{827--841},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Lars Arge and J{\'a}nos Pach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5105},
  URN =		{urn:nbn:de:0030-drops-51052},
  doi =		{10.4230/LIPIcs.SOCG.2015.827},
  annote =	{Keywords: Persistent Homology, Topological Data Analysis, Scalar Field Analysis, Nested Rips Filtration, Distance to a Measure}
}

Keywords: Persistent Homology, Topological Data Analysis, Scalar Field Analysis, Nested Rips Filtration, Distance to a Measure
Collection: 31st International Symposium on Computational Geometry (SoCG 2015)
Issue Date: 2015
Date of publication: 12.06.2015

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