文章基本信息

标题：The VC Dimension of Metric Balls Under Fréchet and Hausdorff Distances
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作者：Anne Driemel ; Jeff M. Phillips ; Ioannis Psarros 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：129
页码：1-16
DOI：10.4230/LIPIcs.SoCG.2019.28
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The Vapnik-Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in R^d and the sets {R} are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.
关键词：VC dimension; Fréchet distance; Hausdorff distance