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.

翻译：通常使用网络来编码物理、生物、社会科学及信息科学等领域复杂系统中实体间的交互架构。为研究复杂系统的大尺度行为，有必要考察网络中作为影响此类行为构建模块的中尺度结构。我们提出一种描述网络中低秩中尺度结构的新方法，并通过若干合成网络模型以及经验性友谊网络、合作网络和蛋白质-蛋白质相互作用（PPI）网络来阐释该方法。研究发现这些网络包含数量相对较少的"潜在模体"，这些模体共同作用下能够成功逼近固定中尺度下网络中的大部分子图。我们采用"网络字典学习"（NDL）算法（该算法结合了网络采样方法与非负矩阵分解）来学习给定网络的潜在模体。利用一组潜在模体编码网络的能力可广泛适用于网络分析任务（如比较、去噪和边推断）。此外，通过新型网络去噪与重建（NDR）算法，我们展示了如何仅利用直接从受损网络中学习到的潜在模体来去除网络噪声。