论文标题
广义定位物和图基因
Generalized Permutants and Graph GENEOs
论文作者
论文摘要
在本文中，我们在拓扑数据分析和几何深度学习之间建立了一个桥梁，从而适应了群体模棱两可的非企业运算符（Geneos）的拓扑理论，以作用于在顶点或边缘加权的所有图表的空间。这是通过展示Geneo的一般概念如何用于转换图形并提供有关其结构的信息来完成的。这就需要引入广义定义和广义定义措施的新概念以及这些概念使我们能够在图之间构建基因的数学证据。实验部分结束了本文，说明了我们的操作员可能使用从图形中提取信息。本文是致力于为几何深度学习开发基因诺斯的组成和几何理论的研究线的一部分。
In this paper we establish a bridge between Topological Data Analysis and Geometric Deep Learning, adapting the topological theory of group equivariant non-expansive operators (GENEOs) to act on the space of all graphs weighted on vertices or edges. This is done by showing how the general concept of GENEO can be used to transform graphs and to give information about their structure. This requires the introduction of the new concepts of generalized permutant and generalized permutant measure and the mathematical proof that these concepts allow us to build GENEOs between graphs. An experimental section concludes the paper, illustrating the possible use of our operators to extract information from graphs. This paper is part of a line of research devoted to developing a compositional and geometric theory of GENEOs for Geometric Deep Learning.
