Contagion Dynamics for Manifold Learning - Mahler, Barbara I. (Frontiers in Big Data, 2022)
3 Contagion maps exploit activation times in threshold contagions to assign vectors in high- 4 dimensional Euclidean space to the nodes of a network. A point cloud that is the image of a 5 contagion map reflects both the structure underlying the network and the spreading behaviour 6 of the contagion on it. Intuitively, such a point cloud exhibits features of the network’s underlying 7 structure if the contagion spreads along that structure, an observation which suggests contagion 8 maps as a viable manifold-learning technique. We test contagion maps and variants thereof as 9 a manifold-learning tool on a number of different synthetic and real-world data sets, and we 10 compare their performance to that of Isomap, one of the most well-known manifold-learning 11 algorithms. We find that, under certain conditions, contagion maps are able to reliably detect 12 underlying manifold structure in noisy data, while Isomap fails due to noise-induced error. This 13 consolidates contagion maps as a technique for manifold learning. We also demonstrate that 14 processing distance estimates between data points before performing methods to determine 15 geometry, topology and dimensionality of a data set leads to clearer results for both Isomap and 16 contagion maps.