Clustering of big data: Consistency of a nonlocal ginzburg-landau type model

After introducing the main ideas and reviewing some of the literature on the subject, we consider a discrete non-local variational model for clustering in the context of soft-classification semi-supervised learning. The functional is inspired by a similar model studied by Alberti and Bellettini (see [1]) in the context of phase transition for ferromagnetic materials. A parameter ϵ_ncontrols both the non-local term, as well as the size of the phase transition layer. We identify the G-limit of the variational functional as ϵ_n→ 0. In the machine learning community, this is known as the study of the consistency of the model. The limiting functional is given by a fidelity term plus weighted anisotropic perimeter.