  Data Science aims to extract meaningful knowledge from unorganised data. Real
datasets usually come in the form of a cloud of points with only pairwise
distances. Numerous applications require 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 a shape of
the cloud. This paper compares several 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 algorithm produces a Homologically Persistent
Skeleton (HoPeS) for any cloud without extra parameters. This universal
skeleton contains sub-graphs 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.
