@kirk86

The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances

, , and . (2019)cite arxiv:1903.03211Comment: 23 pages, 5 figures.

Abstract

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.

Description

[1903.03211] The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances

Links and resources

URL:
BibTeX key:
driemel2019dimension
search on:

Comments and Reviews  
(0)

There is no review or comment yet. You can write one!

Tags


Cite this publication