In this paper, we consider the simplest class of stratified spaces -- linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding. The algorithm is implemented in the Julia package http://github.com/yossibokor/Skyler.jl , which we used for the numerical simulations in this paper.

中文翻译：

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走向分层空间学习：线性嵌入图

在本文中，我们考虑了最简单的分层空间类别-线性嵌入图。我们提出了一种算法，该算法可学习嵌入式图的抽象结构，并根据从中采样的点云对特定的嵌入进行建模。我们使用了来自计算几何，代数拓扑和拓扑数据分析的工具和灵感，并在嵌入的假设下证明了所识别的抽象结构的正确性。该算法在Julia包http://github.com/yossibokor/Skyler.jl中实现，我们在本文中将其用于数值模拟。