Learning low-rank latent mesoscale structures in networks

TL;DR

This paper introduces a novel low-rank mesoscale structure modeling approach for networks, using network dictionary learning to identify latent motifs that efficiently approximate and analyze complex network data.

Contribution

It proposes a new method combining network sampling and nonnegative matrix factorization to learn latent mesoscale motifs, enabling improved network analysis and denoising.

Findings

Networks have few latent motifs that approximate subgraphs

The method effectively denoises and reconstructs corrupted networks

Latent motifs facilitate network comparison and inference

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.