## Abstract

The consistency of a non-local 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 functions, and the p-Laplacian, that enforces regularity. Under appropriate scaling between the two terms, minimisers exhibit a phase transition on the order of = _{n}, where n is the number of data points. We study the large data asymptotics, i.e. as n, in the regime where _{n} 0. The mathematical tool used to address this question is "-convergence. It is proved that the discrete model converges to a weighted anisotropic perimeter.

Original language | English |
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Pages (from-to) | 1-47 |

Number of pages | 47 |

Journal | European Journal of Applied Mathematics |

Early online date | 14 Nov 2018 |

DOIs | |

Publication status | E-pub ahead of print - 14 Nov 2018 |

## Keywords

- "-convergence
- Ginzburg-Landau functional
- non-local variational problems
- PDEs on graphs
- phase transitions

## ASJC Scopus subject areas

- Applied Mathematics