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Large data limit for a phase transition model with the p-Laplacian on point clouds by Cristoferi, Riccardo; Thorpe, Matthew is a scholarly article available to read on EtoBox.

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

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. 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 model converges to a weighted anisotropic perimeter.

Author

Cristoferi, Riccardo; Thorpe, Matthew

Published

2018

Language

EN