Network embedding has been widely employed in networked data mining applications as it can learn low-dimensional and dense node representations from the high-dimensional and sparse network structure. While most existing network embedding methods only model the proximity between two nodes regardless of the order of the proximity, this paper proposes to explicitly model multi-node proximities which can be widely observed in practice, e.g., multiple researchers coauthor a paper, and multiple genes co-express a protein. Explicitly modeling multi-node proximities is important because some two-node interactions may not come into existence without a third node. By proving that LINE(1st), a recent network embedding method, is equivalent to kernelized matrix factorization, this paper proposes coupled kernelized multi-dimensional array factorization (Cetera) which jointly factorizes multiple multi-dimensional arrays by enforcing a consensus representation for each node. In this way, node representations can be more comprehensive and effective, which is demonstrated on three real-world networks through link prediction and multi-label classification.

中文翻译：

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通过耦合核化多维数组分解的网络嵌入

网络嵌入已广泛用于网络数据挖掘应用程序，因为它可以从高维稀疏网络结构中学习低维密集节点表示。虽然大多数现有的网络嵌入方法只对两个节点之间的邻近度进行建模，而不管邻近度的顺序，但本文提出明确建模多节点邻近度，这在实践中可以广泛观察到，例如，多个研究人员合着一篇论文，以及多个基因共表达蛋白质。显式建模多节点邻近性很重要，因为如果没有第三个节点，一些双节点交互可能不会存在。通过证明最近的网络嵌入方法 LINE(1st) 等价于核化矩阵分解，本文提出了耦合核化多维数组分解（Cetera），它通过强制每个节点的共识表示来联合分解多个多维数组。通过这种方式，节点表示可以更加全面和有效，这在三个真实世界的网络上通过链接预测和多标签分类得到了证明。