Data Science aims to extract meaningful knowledge from unorganised data. Real datasets usually come in the form of a cloud of points. It is a requirement of numerous applications to visualise an overall shape of a noisy cloud of points sampled from a non-linear object that is more complicated than a union of disjoint clusters. The skeletonisation problem in its hardest form is to find a 1-dimensional skeleton that correctly represents the shape of the cloud.

This paper compares different algorithms that solve the above skeletonisation problem for any point cloud and guarantee a successful reconstruction. For example, given a highly noisy point sample of an unknown underlying graph, a reconstructed skeleton should be geometrically close and homotopy equivalent to (has the same number of independent cycles as) the underlying graph.

One of these algorithms produces a Homologically Persistent Skeleton (HoPeS) for any cloud without extra parameters. This universal skeleton contains subgraphs that provably represent the 1-dimensional shape of the cloud at any scale. Other subgraphs of HoPeS reconstruct an unknown graph from its noisy point sample with a correct homotopy type and within a small offset of the sample. The extensive experiments on synthetic and real data reveal for the first time the maximum level of noise that allows successful graph reconstructions.

数据科学旨在从无组织的数据中提取有意义的知识。实际数据集通常以点云的形式出现。可视化从非线性对象采样的点的嘈杂点云的整体形状，这要比可视化不交集的簇更为复杂，这是许多应用程序的要求。最困难的形式的骨架化问题是找到正确表示云形状的一维骨架。

本文比较了解决上述任何点云的骨架化问题并保证成功重建的不同算法。例如，给定未知基础图的高噪声点样本，则重构的骨架在几何上应接近并且同伦等效于（具有与基础图相同的独立循环数）。

这些算法之一可为任何云生成同质持久骨架（HoPeS），而无需额外参数。这个通用骨架包含子图，可证明以任何比例表示云的一维形状。HoPeS的其他子图根据其噪声点样本以正确的同伦类型在样本的较小偏移范围内重建未知图。在合成和真实数据上进行的广泛实验首次揭示了允许成功进行图形重建的最大噪声水平。