Uniform convergence rates for Lipschitz learning on graphs

Lipschitz learning is a graph-based semi-supervised method where one extends labels from labeled to an unlabeled data set by solving the infinity Laplace equation on weighted graph. In this work we prove uniform convergence rates for solutions of graph as number vertices grows infinity. Their continuum limits are absolutely minimizing extensions with respect geodesic metric domain sampled from. We under very general assumptions weights, vertices, and domain. Our main contribution that obtain quantitative even sparsely connected graphs, they typically appear in applications like learning. particular, our framework allows bandwidths down connectivity radius. For proving first show statement distance functions continuum. Using "comparison functions" principle, can pass these statements harmonic extensions.