On anisotropic diffusion equations for label propagation
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In many problems in data classification one wishes to assign labels to points in a point cloud with a certain number of them being already correctly labeled. In this paper, we propose a microscopic ODE approach, in which information about correct labels is propagated to neighboring points. Its dynamics are based on alignment mechanisms, which are often used in collective and consensus models. We derive the respective continuum description, which corresponds to an anisotropic diffusion equation with reaction term. Solutions of the continuum model inherit interesting properties of the underlying point cloud. We discuss these analytic properties and exemplify the results with micro- and macroscopic simulations.
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