Data driven estimation of Laplace-Beltrami operator
  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. 
Fr\'ed\'eric Chazal (DATASHAPE), Ilaria Giulini (DATASHAPE), Bertrand   Michel (LSTA)
cs.CG cs.LG math.ST stat.TH