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Anomaly detection in dynamic graphs presents a significant challenge due to the temporal evolution of graph structures and attributes. The conventional approaches that tackle this problem typically employ an unsupervised learning framework, capturing normality patterns with exclusive normal data during training and identifying deviations as anomalies during testing. However, these methods face critical drawbacks: they either only depend on proxy tasks for representation without directly pinpointing normal patterns, or they neglect to differentiate between spatial and temporal normality patterns. More recent methods that use contrastive learning with negative sampling also face high computational costs, limiting their scalability to large graphs. To address these challenges, we introduce a novel Spatial-Temporal memories-enhanced graph autoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs) and gated temporal convolution layers to extract spatial and temporal features. Then STRIPE incorporates separate spatial and temporal memory networks to capture and store prototypes of normal patterns, respectively. These stored patterns are retrieved and integrated with encoded graph embeddings through a mutual attention mechanism. Finally, the integrated features are fed into the decoder to reconstruct the graph streams which serve as the proxy task for anomaly detection. This comprehensive approach not only minimizes reconstruction errors but also emphasizes the compactness and distinctiveness of the embeddings w.r.t. the nearest memory prototypes. Extensive experiments on six benchmark datasets demonstrate the effectiveness and efficiency of STRIPE, where STRIPE significantly outperforms existing methods with 5.8% improvement in AUC scores and 4.62X faster in training time.

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities., Comment: v1: 41 pages; v2: 40 pages ; v3: This version focuses on just subgraph problems (discussions on other classic graph problems can be found in the earlier versions)