论文标题
多层随机点产品图
The multilayer random dot product graph
论文作者
论文摘要
我们提出了被称为随机点产品图的潜在位置网络模型的全面扩展，以容纳多个图形（无论是无向和有向的），它们共享了一个共同的节点子集，并提出了一种将相关的邻接矩阵或其子矩阵共同嵌入合适的潜在空间的方法。建立了有关节点表示的渐近行为的理论结果，这表明在施加线性转换后，这些成果在欧几里得规范中均匀地收敛到带有高斯误差的潜在位置。在此框架内，我们将随机块模型的概括为许多不同的多个图形设置，并通过几个统计推断任务来证明我们的联合嵌入方法的有效性，在这些任务中，我们比竞争对手光谱方法获得了可比性或更好的结果。网络安全示例中显示了对单个图嵌入的链接预测的经验改进。
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for jointly embedding the associated adjacency matrices, or submatrices thereof, into a suitable latent space. Theoretical results concerning the asymptotic behaviour of the node representations thus obtained are established, showing that after the application of a linear transformation these converge uniformly in the Euclidean norm to the latent positions with Gaussian error. Within this framework, we present a generalisation of the stochastic block model to a number of different multiple graph settings, and demonstrate the effectiveness of our joint embedding method through several statistical inference tasks in which we achieve comparable or better results than rival spectral methods. Empirical improvements in link prediction over single graph embeddings are exhibited in a cyber-security example.
