文章基本信息

标题：Topological Analysis of Scalar Fields with Outliers
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作者：Micka{\"e}l Buchet ; Fr{\'e}d{\'e}ric Chazal ; Tamal K. Dey 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：34
页码：827-841
DOI：10.4230/LIPIcs.SOCG.2015.827
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Persistent Homology; Topological Data Analysis; Scalar Field Analysis; Nested Rips Filtration; Distance to a Measure