论文标题
神经网络可以学习持续的同源性特征吗？
Can neural networks learn persistent homology features?
论文作者
论文摘要
拓扑数据分析使用拓扑中的工具 - 研究塑造的数学领域 - 创建数据表示。特别是，在持续的同源性中，一个研究与数据相关的空间的单参数家族，并且持久图描述了拓扑不变性的寿命，例如连接的组件或孔，遍布一个参数家族。在许多应用程序中，人们有兴趣使用与持久图相关的功能而不是图表本身。在我们的工作中，我们探讨了使用神经网络从持久图中提取的几种类型的特征的可能性。
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.
