Shortest path distance in random k-nearest neighbor graphs
Machine Learning
2012-07-10 v2 Machine Learning
Abstract
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.
Cite
@article{arxiv.1206.6381,
title = {Shortest path distance in random k-nearest neighbor graphs},
author = {Morteza Alamgir and Ulrike von Luxburg},
journal= {arXiv preprint arXiv:1206.6381},
year = {2012}
}
Comments
Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)