Point-Level Topological Representation Learning on Point Clouds
Vincent P. Grande and Michael T. Schaub
拓扑数据分析(TDA)允许我们提取关于数据集或点云的全球形状的强大拓扑和高阶信息。 像Persistent Homology或Euller Transform这样的工具对点云的全局结构进行了单一的复杂描述。 然而,分类等常见的机器学习应用程序需要提供点级信息和功能。 在本文中,我们弥合了这一差距,并提出了一种新的方法,利用代数拓扑和微分几何学概念的离散变体从复杂的点云中提取节点级拓扑特征。 我们验证这些拓扑点特征(TOPF)在合成和真实世界数据上的有效性,并研究它们噪声和异构采样下的稳健性。
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topo...