Contagion Dynamics for Manifold Learning

• URL: http://arxiv.org/abs/2012.00091v1
• Date: Mon, 30 Nov 2020 20:58:21 GMT
• Title: Contagion Dynamics for Manifold Learning
• Authors: Barbara I. Mahler
• Abstract summary: Contagion maps exploit activation times in threshold contagions to assign vectors in high-dimensional Euclidean space to the nodes of a network. We test contagion maps as a manifold-learning tool on a number of different real-world and synthetic data sets. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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