Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data, and persistence diagrams describe the lifetime of topological invariants, such as connected components or holes, across the one-parameter family. In many applications, one is interested in working with features associated with persistence diagrams rather than the diagrams themselves. In our work, we explore the possibility of learning several types of features extracted from persistence diagrams using neural networks.

中文翻译：

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神经网络可以学习持久的同源性特征吗？

拓扑数据分析使用拓扑中的工具-研究形状的数学领域-创建数据表示。特别是，在持久性同源性中，一项研究与数据关联的空间的一参数族，而持久性图描述了在一参数族中拓扑不变变量（例如连接的组件或孔）的寿命。在许多应用程序中，人们有兴趣使用与持久性图相关的功能，而不是图本身。在我们的工作中，我们探索了使用神经网络学习从持久性图中提取的几种类型的特征的可能性。