On Anisotropic Diffusion Equations for Label Propagation
In many problems in data classification, it is desirable to assign labels to points in a point cloud where a certain number of them is already correctly labeled. In this talk, we propose a microscopic ODE approach, in which information about correct labels propagates to neighboring points. Its dynamics are based on alignment mechanisms, often used in collective and consensus models. We derive the respective continuum description, which corresponds to an anisotropic diffusion equation with a reaction term. Solutions of the continuum model inherit interesting properties of the underlying point cloud. We discuss the qualitative behavior of solutions and exemplify the results with micro- and macroscopic simulations. This is joint work with Marie-Therese Wolfram.