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The consistency of a nonlocal anisotropic Ginzburg-Landau type functional fordata classification and clustering is studied. The Ginzburg-Landau objectivefunctional combines a double well potential, that favours indicator valuedfunction, and the $p$-Laplacian, that enforces regularity. Under appropriatescaling between the two terms minimisers exhibit a phase transition on theorder of $\epsilon=\epsilon_n$ where $n$ is the number of data points. We studythe large data asymptotics, i.e. as $n\to \infty$, in the regime where$\epsilon_n\to 0$. The mathematical tool used to address this question is$\Gamma$-convergence. In particular, it is proved that the discrete modelconverges to a weighted anisotropic perimeter.

Large data limit for a phase transition model with the p-Laplacian on point clouds