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In this work we begin to rigorously analyze the MBO scheme for dataclustering in the large data limit. Each iteration of the MBO schemecorresponds to one step of implicit gradient descent for the thresholdingenergy on the similarity graph of some dataset. For a subset of the nodes ofthe graph, the thresholding energy at time $h$ is the amount of heattransferred from the subset to its complement at time $h$, rescaled by a factor$\sqrt{h}$. It is then natural to think that outcomes of the MBO scheme are(local) minimizers of this energy. We prove that the algorithm is consistent,in the sense that these (local) minimizers converge to minimizers of a suitablyweighted optimal partition problem.

Large data limit of the MBO scheme for data clustering: $\Gamma$-convergence of the thresholding energies