Networks are prevalent in many areas and are often collected from multiple sources. However, due to the veracity characteristics, more often than not, networks are incomplete. Network alignment and network completion have become two fundamental cornerstones behind a wealth of high-impact graph mining applications. The state-of-the-art have been addressing these two tasks in parallel . That is, most of the existing network alignment methods have implicitly assumed that the topology of the input networks for alignment are perfectly known a priori, whereas the existing network completion methods admit either a single network (i.e., matrix completion) or multiple aligned networks (e.g., tensor completion). In this article, we argue that network alignment and completion are inherently complementary with each other, and hence propose to jointly address them so that the two tasks can mutually benefit from each other. We formulate the problem from the optimization perspective, and propose an effective algorithm ( iNeAt ) to solve it. The proposed method offers two distinctive advantages. First ( Alignment accuracy ), our method benefits from the higher-quality input networks while mitigates the effect of the incorrectly inferred links introduced by the completion task itself. Second ( Alignment efficiency ), thanks to the low-rank structure of the complete networks and the alignment matrix, the alignment process can be significantly accelerated. We perform extensive experiments which show that (1) the network completion can significantly improve the alignment accuracy, i.e., up to 30% over the baseline methods; (2) the network alignment can in turn help recover more missing edges than the baseline methods; and (3) our method achieves a good balance between the running time and the accuracy, and scales with a provable linear complexity in both time and space.

中文翻译：

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不完整的网络对齐

网络在许多领域都很普遍，并且通常从多个来源收集。然而，由于真实性的特点，网络往往是不完整的。网络对齐和网络完成已成为大量高影响图挖掘应用程序背后的两个基本基石。最先进的技术一直在解决这两个任务在平行下. 也就是说，大多数现有的网络对齐方法都隐含地假设用于对齐的输入网络的拓扑是完全已知的，而现有的网络补全方法允许单个网络（即矩阵补全）或多个对齐网络（例如，张量完成）。在本文中，我们认为网络对齐和完成本质上是相互补充的，因此建议联合解决它们，以便这两个任务可以互惠互利。我们从优化的角度制定问题，并提出一个有效的算法（iNeAt) 来解决它。所提出的方法提供了两个明显的优点。第一的 （对准精度)，我们的方法受益于更高质量的输入网络，同时减轻了由完成任务本身引入的错误推断链接的影响。第二 （对齐效率)，得益于完整网络的低秩结构和对齐矩阵，对齐过程可以显着加快。我们进行了广泛的实验，表明（1）网络完成可以显着提高对齐精度，即比基线方法提高 30%；(2) 网络对齐反过来可以帮助恢复比基线方法更多的缺失边缘；(3) 我们的方法在运行时间和准确率之间取得了很好的平衡，并且可以证明线性的时间和空间上的复杂性。