# On anisotropic diffusion equations for label propagation

arXiv: https://arxiv.org/abs/2007.12516 · HTML: https://mlsanity.com/paper/2007.12516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Models for information propagation on graphs](https://mlsanity.com/paper/2201.07577/) (2022)

## Abstract (arXiv)

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 commonly used in large interacting agent systems in consensus formation. We derive the respective continuum description, which corresponds to an anisotropic diffusion equation with reaction term. Solutions of the continuum model on the bounded domain inherit certain properties of the underlying point cloud. We discuss these analytic properties and exemplify the results with micro- and macroscopic simulations.