Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be specified in advance. In this article, a novel Bayesian model for simultaneous and automatic selection of the appropriate dimension of the latent space and the number of blocks is proposed. Extensions to directed and bipartite graphs are discussed. The model is tested on simulated and real world network data, showing promising performance for recovering latent community structure.

中文翻译：

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随机块模型中潜在维度和社区的贝叶斯估计

无向图的邻接或Laplacian矩阵的频谱嵌入是一种在具有最佳理论保证的情况下用于表示低维潜在空间中网络的常用技术。嵌入可用于估计网络的社区结构，在随机块模型框架中具有很强的一致性。用于从频谱嵌入进行社区检测的标准算法的主要实际限制之一是必须预先指定社区的数量和嵌入的潜在维度。在本文中，提出了一种新颖的贝叶斯模型，用于同时自动选择潜在空间的适当尺寸和块数。讨论了有向图和二部图的扩展。该模型已在模拟和现实世界的网络数据上进行了测试，