Hein, M.M.HeinAudibert, J.-Y.J.-Y.AudibertLuxburg, U. vonU. vonLuxburg2022-03-102022-03-102005https://publica.fraunhofer.de/handle/publica/35005710.1007/11503415_322-s2.0-26944489604In the machine learning community it is generally believed that graph Laplacians corresponding to a finite sample of data points converge to a continuous Laplace operator if the sample size increases. Even though this assertion serves as a justification for many Laplacian-based algorithms, so far only some aspects of this claim have been rigorously proved. In this paper we close this gap by establishing the strong pointwise consistency of a family of graph Laplacians with data-dependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of R-d.en004005conference paper