  Approximations of Laplace-Beltrami operators on manifolds through graph
Lapla-cians have become popular tools in data analysis and machine learning.
These discretized operators usually depend on bandwidth parameters whose tuning
remains a theoretical and practical problem. In this paper, we address this
problem for the unnormalized graph Laplacian by establishing an oracle
inequality that opens the door to a well-founded data-driven procedure for the
bandwidth selection. Our approach relies on recent results by Lacour and
Massart [LM15] on the so-called Lepski's method.
