  We prove that the dynamics of the MBO scheme for data clustering converge to
a viscosity solution to mean curvature flow. The main ingredients are (i) a new
abstract convergence result based on quantitative estimates for heat operators
and (ii) the derivation of these estimates in the setting of random geometric
graphs. To implement the scheme in practice, two important parameters are the
number of eigenvalues for computing the heat operator and the step size of the
scheme. The results of the current paper give a theoretical justification for
the choice of these parameters in relation to sample size and interaction
width.
