论文标题
光谱嵌入和多部分网络的潜在几何形状
Spectral embedding and the latent geometry of multipartite networks
论文作者
论文摘要
光谱嵌入基于其邻接或拉普拉斯矩阵的特征向量的网络节点的矢量表示，并在整个科学中发现了应用程序。许多这样的网络都是多部分的，这意味着它们的节点可以分为组，并且同一组的节点永远不会连接。当网络是多部分时，本文证明了通过光谱嵌入获得的节点表示，生存的较高维度环境空间的小组特异性低维子空间附近。因此，我们提出了光谱嵌入后的后续步骤，以在其内在的而不是环境维度中恢复节点表示形式，从而证明在低级别的，不均匀的随机图模型下均匀的一致性。我们的方法自然概括了两分光谱嵌入，其中通过双jaCencenty或Bi-Laplacian矩阵的奇异值分解获得了节点表示。
Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of its adjacency or Laplacian matrix, and has found applications throughout the sciences. Many such networks are multipartite, meaning their nodes can be divided into groups and nodes of the same group are never connected. When the network is multipartite, this paper demonstrates that the node representations obtained via spectral embedding live near group-specific low-dimensional subspaces of a higher-dimensional ambient space. For this reason we propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension, proving uniform consistency under a low-rank, inhomogeneous random graph model. Our method naturally generalizes bipartite spectral embedding, in which node representations are obtained by singular value decomposition of the biadjacency or bi-Laplacian matrix.
