文章基本信息

标题：Geometric Inference on Kernel Density Estimates
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作者：Jeff M. Phillips ; Bei Wang ; Yan Zheng 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：857-871
DOI：10.4230/LIPIcs.SOCG.2015.857
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance, which isomorphically map to superlevel sets of the kernel density estimate. We prove new properties about the kernel distance, demonstrating stability results and allowing it to inherit reconstruction results from recent advances in distance-based topological reconstruction. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes.
关键词：topological data analysis; kernel density estimate; kernel distance