AUTHOR=Mahler Barbara I. 

TITLE=Contagion Dynamics for Manifold Learning

JOURNAL=Frontiers in Big Data

VOLUME=Volume 5 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/big-data/articles/10.3389/fdata.2022.668356

DOI=10.3389/fdata.2022.668356

ISSN=2624-909X

ABSTRACT=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.