Learning on varifolds

In this paper, we propose a new learning framework based on the mathematical concept of varifolds (Morgan, 2000), which are the measure-theoretic generalization of differentiable manifolds. We compare varifold learning with the popular manifold learning and demonstrate some of its specialties. Algorithmically, we derive a neighborhood refinement technique for hypergraph models, which is conceptually analogous to varifolds, give the procedure for constructing such hypergraphs from data and finally by using the hypergraph Laplacian matrix we are able to solve high-dimensional classification problems accurately.