This work considers a practical semi-supervised graph anomaly detection (GAD)
scenario, where part of the nodes in a graph are known to be normal,
contrasting to the unsupervised setting in most GAD studies with a fully
unlabeled graph. As expected, we find that having access to these normal nodes
helps enhance the detection performance of existing unsupervised GAD methods
when they are adapted to the semi-supervised setting. However, their
utilization of these normal nodes is limited. In this paper, we propose a novel
Generative GAD approach (GGAD) for the semi-supervised scenario to better
exploit the normal nodes. The key idea is to generate outlier nodes that
assimilate anomaly nodes in both local structure and node representations for
providing effective negative node samples in training a discriminative
one-class classifier. There have been many generative anomaly detection
approaches, but they are designed for non-graph data, and as a result, they
fail to take account of the graph structure information. Our approach tackles
this problem by generating graph structure-aware outlier nodes that have
asymmetric affinity separability from normal nodes while being enforced to
achieve egocentric closeness to normal nodes in the node representation space.
Comprehensive experiments on four real-world datasets are performed to
establish a benchmark for semi-supervised GAD and show that GGAD substantially
outperforms state-of-the-art unsupervised and semi-supervised GAD methods with
varying numbers of training normal nodes. Code will be made available at
this https URL

本研究提出了一种新颖的半监督场景下的图异常检测方法（GGAD），通过生成能够在本地结构和节点表示中模拟异常节点的异常节点，为训练具有区分性的单类分类器提供有效的负节点样本，从而更好地利用已知的正常节点。在四个真实世界数据集上进行了全面的实验，建立了半监督图异常检测方法的基准，并展示了 GGAD 在不同数量训练正常节点下大大优于最先进的无监督和半监督图异常检测方法。

生成半监督图异常检测

Generative Semi-supervised Graph Anomaly Detection

Community detection, which aims to cluster $N$ nodes in a given graph into
$r$ distinct groups based on the observed undirected edges, is an important
problem in network data analysis. In this paper, the popular stochastic block
model (SBM) is extended to the generalized stochastic block model (GSBM) that
allows for adversarial outlier nodes, which are connected with the other nodes
in the graph in an arbitrary way. Under this model, we introduce a procedure
using convex optimization followed by $k$-means algorithm with $k=r$. Both
theoretical and numerical properties of the method are analyzed. A theoretical
guarantee is given for the procedure to accurately detect the communities with
small misclassification rate under the setting where the number of clusters can
grow with $N$. This theoretical result admits to the best-known result in the
literature of computationally feasible community detection in SBM without
outliers. Numerical results show that our method is both computationally fast
and robust to different kinds of outliers, while some popular computationally
fast community detection algorithms, such as spectral clustering applied to
adjacency matrices or graph Laplacians, may fail to retrieve the major clusters
due to a small portion of outliers. We apply a slight modification of our
method to a political blogs data set, showing that our method is competent in
practice and comparable to existing computationally feasible methods in the
literature. To the best of the authors' knowledge, our result is the first in
the literature in terms of clustering communities with fast growing numbers
under the GSBM where a portion of arbitrary outlier nodes exist.

本研究将随机块模型扩展到广义随机块模型，提出了一种使用凸优化和 k 均值算法的程序，用于在存在离群节点的情况下，准确检测社区的聚类。