Motivated by social network analysis and network-based recommendation systems, we study a semi-supervised community detection problem in which the objective is to estimate the community label of a new node using the network topology and partially observed community labels of existing nodes. The network is modeled using a degree-corrected stochastic block model, which allows for severe degree heterogeneity and potentially non-assortative communities. We propose an algorithm that computes a `structural similarity metric' between the new node and each of the $K$ communities by aggregating labeled and unlabeled data. The estimated label of the new node corresponds to the value of $k$ that maximizes this similarity metric. Our method is fast and numerically outperforms existing semi-supervised algorithms. Theoretically, we derive explicit bounds for the misclassification error and show the efficiency of our method by comparing it with an ideal classifier. Our findings highlight, to the best of our knowledge, the first semi-supervised community detection algorithm that offers theoretical guarantees.

本文提出了一种半监督社区检测算法，该算法利用网络拓扑和部分已知社区标签对新节点进行社区标签估计。该算法使用修正节点度数的随机块模型来对网络进行建模，并计算新节点与每个社区之间的结构相似度指标，从而预测新节点的社区标签。该算法在理论和实践中均证明了其有效性，是首个提供理论保证的半监督社区检测算法。

基于结构相似度度量的半监督社区发现