Learning low-rank latent mesoscale structures in networks

• URL: http://arxiv.org/abs/2102.06984v5
• Date: Thu, 13 Jul 2023 05:42:06 GMT
• Title: Learning low-rank latent mesoscale structures in networks
• Authors: Hanbaek Lyu, Yacoub H. Kureh, Joshua Vendrow, Mason A. Porter
• Abstract summary: We present a new approach for describing low-rank mesoscale structures in networks. We use several synthetic network models and empirical friendship, collaboration, and protein--protein interaction (PPI) networks. We show how to denoise a corrupted network by using only the latent motifs that one learns directly from the corrupted network.
• Score: 1.1470070927586016
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is common to use networks to encode the architecture of interactions between entities in complex systems in the physical, biological, social, and information sciences. To study the large-scale behavior of complex systems, it is useful to examine mesoscale structures in networks as building blocks that influence such behavior. We present a new approach for describing low-rank mesoscale structures in networks, and we illustrate our approach using several synthetic network models and empirical friendship, collaboration, and protein--protein interaction (PPI) networks. We find that these networks possess a relatively small number of `latent motifs' that together can successfully approximate most subgraphs of a network at a fixed mesoscale. We use an algorithm for `network dictionary learning' (NDL), which combines a network-sampling method and nonnegative matrix factorization, to learn the latent motifs of a given network. The ability to encode a network using a set of latent motifs has a wide variety of applications to network-analysis tasks, such as comparison, denoising, and edge inference. Additionally, using a new network denoising and reconstruction (NDR) algorithm, we demonstrate how to denoise a corrupted network by using only the latent motifs that one learns directly from the corrupted network.

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