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

Understand

The consistency of a nonlocal anisotropic Ginzburg-Landau type functional for data classification and clustering is studied.

• The Ginzburg-Landau objective functional combines a double well potential, that favours indicator valued function, and the $p$-Laplacian, that enforces regularity.
• Under appropriate scaling between the two terms minimisers exhibit a phase transition on the order of $\epsilon=\epsilon_n$ where $n$ is the number of data points.
• We study the large data asymptotics, i.e.