Contagion Dynamics for Manifold Learning

TL;DR

Contagion maps utilize contagion spreading patterns to effectively uncover underlying manifold structures in complex networks, outperforming traditional methods like Isomap especially in noisy data scenarios.

Contribution

This paper introduces contagion maps as a novel manifold-learning technique and demonstrates their robustness and effectiveness compared to existing methods.

Findings

Contagion maps reliably detect manifold structures in noisy data.

They outperform Isomap in certain conditions.

Contagion maps are validated on real-world and synthetic datasets.

Abstract

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.