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：常通过编码复杂系统（涵盖物理、生物、社会科学及信息科学领域）中实体间交互架构的网络来研究其行为。为探究复杂系统的大尺度行为，有必要将网络中作为影响此类行为的构建模块——介观结构纳入考察。我们提出了一种描述网络中低秩介观结构的新方法，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)网络对其进行了验证。研究发现，这些网络仅需少量"潜在基元"即可在固定介观尺度上成功逼近大多数子图。我们采用结合网络采样方法与非负矩阵分解的"网络字典学习"(NDL)算法进行网络潜在基元的提取。利用潜在基元集合编码网络的能力可广泛应用于网络分析任务，包括网络比较、去噪及边推断。此外，通过新型网络去噪与重构(NDR)算法，我们展示了如何仅利用从受损网络中直接习得的潜在基元实现网络去噪。