Contagion Dynamics for Manifold Learning
This work provides a new method for manifold learning, particularly beneficial for researchers dealing with noisy network data where traditional methods like Isomap struggle.
This paper explores the use of contagion maps, which assign high-dimensional Euclidean vectors to network nodes based on activation times in threshold contagions, as a manifold-learning technique. The authors demonstrate that contagion maps can reliably detect underlying manifold structure in noisy data, outperforming Isomap under specific noisy conditions.
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.