Link prediction -- the process of uncovering missing links in a complex network -- is an important problem in information sciences, with applications ranging from social sciences to molecular biology. Recent advances in neural graph embeddings have proposed an end-to-end way of learning latent vector representations of nodes, with successful application in link prediction tasks. Yet, our understanding of the internal mechanisms of such approaches has been rather limited, and only very recently we have witnessed the development of a very compelling connection to the mature matrix factorization theory. In this work, we make an important contribution to our understanding of the interplay between the skip-gram powered neural graph embedding algorithms and the matrix factorization via SVD. In particular, we show that the link prediction accuracy of graph embeddings strongly depends on the transformations of the original graph co-occurrence matrix that they decompose, sometimes resulting in staggering boosts of accuracy performance on link prediction tasks. Our improved approach to learning low-rank factorization embeddings that incorporate information from unlikely pairs of nodes yields results on par with the state-of-the-art link prediction performance achieved by a complex neural graph embedding model

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通过矩阵分解进行链接预测的图嵌入：平滑或截断负数？

链接预测——发现复杂网络中缺失链接的过程——是信息科学中的一个重要问题，其应用范围从社会科学到分子生物学。神经图嵌入的最新进展提出了一种学习节点潜在向量表示的端到端方法，并成功应用于链接预测任务。然而，我们对这些方法的内部机制的理解相当有限，直到最近我们才目睹了与成熟矩阵分解理论之间非常引人注目的联系的发展。在这项工作中，我们对理解skip-gram 驱动的神经图嵌入算法和通过SVD 进行矩阵分解之间的相互作用做出了重要贡献。特别是，我们表明图嵌入的链接预测精度在很大程度上取决于它们分解的原始图共生矩阵的转换，有时会导致链接预测任务的精度性能的惊人提升。我们改进的学习低秩分解嵌入的方法结合了来自不太可能的节点对的信息，产生的结果与复杂神经图嵌入模型实现的最先进的链接预测性能相当