Large Data Limit of the MBO Scheme for Data Clustering

Abstract

The MBO scheme is a highly performant scheme used for data clustering and other applications in machine learning. We report on the first theoretical studies of the scheme in the large data limit. Our results relate (i) the final state of the scheme to minimal surfaces in the data manifold and (ii) the dynamics of the scheme to the steepest descent for surfaces, which is mean curvature flow. The tools employed are variational methods for (i) and viscosity solution techniques for (ii).