# Learning low-rank latent mesoscale structures in networks

13 Feb 2021  ·  , , , ·

It is common to use networks to encode the architecture of interactions between entities in complex systems in applications in the physical, biological, social, and information sciences. To study the large-scale behavior of complex systems, it is useful to study mesoscale structures in networks as building blocks that influence such behavior. We present a new approach for describing low-rank mesoscale structure 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 that we call 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 our 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 networks.

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