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The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities.
Definable families of finite Vapnik Chernonenkis dimension
H. Johnson · 1903
Earlier work this paper cites.
On the uniform convergence of relative frequencies of events to their probabilities
V. N. Vapnik and A. Ya. Chervonenkis · 1971
Earlier work this paper cites.
Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth · 1989
Earlier work this paper cites.
A deterministic view of random sampling and its use in geometry
B. Chazelle and J. Friedman · 1990
Earlier work this paper cites.
Concept learning with geometric hypotheses
D. P. Dobkin and D. Gunopulos · 1995
Earlier work this paper cites.
Lectures in Discrete Geometry
J. Matoušek · 2002
Earlier work this paper cites.
The VC dimension of k-fold union
D. Eisenstat and D. Angluin · 2006
Cited alongside, same era.
k k -fold unions of low-dimensional concept classes
D. Eisenstat · 2009
Cited alongside, same era.
A unified framework for approximating and clustering data
D. Feldman and M. Langberg · 2011
Cited alongside, same era.
Tight lower bounds for the size of epsilon-nets
J. Pach and G. Tardos · 2012
Cited alongside, same era.
Distributed k-means and k-median clustering on general topologies
M.-F. Balcan, S. Ehrlich, and Y. Liang · 2013
Cited alongside, same era.
New lower bounds for epsilon-nets
A. Kupavskii, N. H. Mustafa, and J. Pach · 2016
Later among the works it cites.
Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures
M. Lucic, O. Bachem, and A. Krause · 2016
Later among the works it cites.
Scalable and distributed clustering via lightweight coresets
O. Bachem, M. Lucic, and A. Krause · 2017
Later among the works it cites.
Decomposing arrangements of hyperplanes: VC-dimension, combinatorial dimension, and point location
E. Ezra, S. Har-Peled, H. Kaplan, and M. Sharir · 2017
Later among the works it cites.
Sampling for Large-Scale Clustering
O. Bachem · 2018
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