流行度调整区组模型是广义随机点积图
Popularity Adjusted Block Models are Generalized Random Dot Product Graphs
摘要：
我们连接两个随机图模型，流行度调整块模型（PABM）和广义随机点积图（GRDPG），通过证明PABM是GRDPG的一个特殊情况下，社区对应于相互正交的潜向量子空间。这一见解使我们能够构建新的算法社区检测和参数估计的PABM，以及改善现有的算法，依赖于稀疏子空间聚类。使用建立的渐近性质的邻接谱嵌入的GRDPG，我们推导出这些算法的渐近性质。特别是，我们证明了社区检测错误的绝对数量趋于零，图的顶点数趋于无穷大。仿真实验说明了这些属性。
英文摘要：
We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties.
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