v1v2 (latest)
Shortest path distance in random k-nearest neighbor graphs
International Conference on Machine Learning (ICML), 2012
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.
View on arXivComments on this paper
