论文标题
在各向异性扩散方程上的标签传播方程
On anisotropic diffusion equations for label propagation
论文作者
论文摘要
在数据分类的许多问题中，希望将标签分配给点云中的点，其中一定数量的标签已经正确标记。在本文中，我们提出了一种微观颂歌方法，其中有关正确标签的信息传播到相邻点。它的动力学基于对齐机制，该机制通常用于共识形成中的大型交互剂系统。我们得出相应的连续描述，该描述对应于具有反应项的各向异性扩散方程。连续模型的解决方案在有限域上继承了基础云的某些属性。我们讨论了这些分析特性，并用微观和宏观模拟来说明结果。
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.
