Variational limits of k-NN graph based functionals on data clouds [article]

Nicolas Garcia Trillos
2018 arXiv   pre-print
This paper studies the large sample asymptotics of data analysis procedures based on the optimization of functionals defined on k-NN graphs on point clouds. The paper is framed in the context of minimization of balanced cut functionals, but our techniques, ideas and results can be adapted to other functionals of relevance. We rigorously show that provided the number of neighbors in the graph k:=k_n scales with the number of points in the cloud as n ≫ k_n ≫(n), then with probability one, the
more » ... tion to the graph cut optimization problem converges towards the solution of an analogue variational problem at the continuum level.
arXiv:1607.00696v3 fatcat:jlpluziv7rgyhhk2jc42dii23y