Shortest path distance in random k-nearest neighbor graphs

Morteza Alamgir; Ulrike von Luxburg

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arXiv · 1206.6381

Shortest path distance in random k-nearest neighbor graphs

Morteza Alamgir·Ulrike von Luxburg

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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.

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Morteza Alamgir, Ulrike von Luxburg. 2012-07-09. Shortest path distance in random k-nearest neighbor graphs. https://arxiv.org/abs/1206.6381

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