关于各向异性扩散方程的标号传播
On anisotropic diffusion equations for label propagation
摘要：
在数据分类的许多问题中，人们希望为点云中的点分配标签，其中一定数量的点已经被正确标记。在本文中，我们提出了一个微观的ODE方法，在该方法中，正确的标签的信息传播到相邻的点。它的动力学是基于对齐机制，这是常用的大型互动代理系统的共识形成。我们推导出相应的连续描述，它对应于一个各向异性的扩散方程与反应项。有界域上的连续体模型的解继承了底层点云的某些性质。我们讨论了这些分析性质，并将结果与微观和宏观模拟。
英文摘要：
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.
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