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Publication 18-CNA-004
R. Cristoferi Matthew Thorpe Abstract: 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
$\varepsilon$ = $\varepsilon_n$ where $n$ is the number of data points. We study the large data asymptotics, i.e. as $n \to \infty$,
in the regime where $\varepsilon_n \to 0$. 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.Get the paper in its entirety as 18-CNA-004.pdf |