学习网络中的低秩潜在中尺度结构
Learning low-rank latent mesoscale structures in networks
AI总结：
本文提出结合网络采样与非负矩阵分解的NDL方法，从合成及真实网络中学习少量潜在基序以表示低秩中尺度结构，并通过NDR算法实现受损网络去噪与重建。
摘要：
在物理、生物、社会和信息科学中，人们通常使用网络来编码复杂系统中实体之间交互的架构。为研究复杂系统的大规模行为，考察网络中的中尺度结构是有益的，这些结构是影响此类行为的构建块。我们提出了一种描述网络中低秩中尺度结构的新方法，并利用若干合成网络模型以及经验性的友谊、合作和蛋白质-蛋白质相互作用（PPI）网络来说明该方法。我们发现，这些网络拥有数量相对较少的“潜在基序”，它们共同能够在固定中尺度上成功逼近网络的大多数子图。我们使用一种“网络字典学习”（NDL）算法来学习给定网络的潜在基序，该算法结合了网络采样方法和非负矩阵分解。利用一组潜在基序编码网络的能力，可广泛应用于网络比较、去噪和边推断等网络分析任务。此外，利用一种新的网络去噪与重建（NDR）算法，我们展示了如何仅凭借直接从受损网络中学习到的潜在基序，对受损网络进行去噪。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
