  Contagion maps exploit activation times in threshold contagions to assign
vectors in high-dimensional Euclidean space to the nodes of a network. A point
cloud that is the image of a contagion map reflects both the structure
underlying the network and the spreading behaviour of the contagion on it.
Intuitively, such a point cloud exhibits features of the network's underlying
structure if the contagion spreads along that structure, an observation which
suggests contagion maps as a viable manifold-learning technique. We test
contagion maps as a manifold-learning tool on a number of different real-world
and synthetic data sets, and we compare their performance to that of Isomap,
one of the most well-known manifold-learning algorithms. We find that, under
certain conditions, contagion maps are able to reliably detect underlying
manifold structure in noisy data, while Isomap fails due to noise-induced
error. This consolidates contagion maps as a technique for manifold learning.
