论文标题
在TDA中构建小组非企业运算符的一些新方法
Some new methods to build group equivariant non-expansive operators in TDA
论文作者
论文摘要
小组模棱两可的运营商在机器学习和拓扑数据分析中起着越来越相关的作用。在本文中，我们提出了一些有关$ g $ equivariant非企业运算符（Geneos）的新结果，该结果是从拓扑空间$ x $ to $ \ \ varphi $本身上的真实价值有限的连续功能的空间$ \ varphi $中的。 Space $ \ varphi $代表我们的一组数据，而$ g $是$ x $的所有自我塑料的组的子组，代表了我们感兴趣的不变性。
Group equivariant operators are playing a more and more relevant role in machine learning and topological data analysis. In this paper we present some new results concerning the construction of $G$-equivariant non-expansive operators (GENEOs) from a space $\varPhi$ of real-valued bounded continuous functions on a topological space $X$ to $\varPhi$ itself. The space $\varPhi$ represents our set of data, while $G$ is a subgroup of the group of all self-homeomorphisms of $X$, representing the invariance we are interested in.
