Detecting anomalous nodes in continuously evolving graphs without labeled supervision requires representations that capture both local temporal context and globally consistent normal behavior—a combination that current methods do not jointly address. Existing dynamic anomaly detectors rely on localized temporal neighborhoods and cannot leverage globally similar normal patterns elsewhere in the graph, while existing retrieval-augmented graph methods either require labels or do not enforce strict temporal causality during retrieval. We propose DGRA-CL (Dynamic Graph Retrieval-Augmented Contrastive Learning), an unsupervised framework that learns discriminative temporal node representations for anomaly detection without labeled data. DGRA-CL transforms dynamic graphs into temporal sequences, employs time- and context-aware contrastive learning to learn normal node behavior patterns, retrieves similar normal exemplars from a training pool under a strict causality constraint, and fuses them via similarity-weighted aggregation to construct baseline representations. Anomalies are detected via deviation-based scoring measuring distance from these normal baselines. On four real-world dynamic graphs, DGRA-CL achieves statistically significant AUC gains of 1–2 points over the strongest baselines on three of four benchmarks (UCI Messages, Bitcoin-Alpha, Digg) and competitive performance on Reddit, while operating without anomaly labels and generalizing to unseen nodes.

Knowledge Tracing (KT) models aim to predict student performance from interaction histories in order to support personalised learning. However, many learners generate only limited interaction data, making reliable knowledge-state estimation difficult. Recent contrastive KT methods attempt to address this data sparsity through self-supervised representation learning from augmented versions of individual learner sequences, operating within an intra-learner paradigm, where contrastive signals are derived solely from variations of a single learner's trajectory. We advance prior work by proposing RACL (Retrieval-Augmented Contrastive Learning), a knowledge tracing framework that introduces an inter-learner contrastive paradigm, leveraging the observation that students with similar skill profiles often exhibit comparable learning trajectories. Cross-learner structure therefore provides naturally occurring positive and negative examples that are more pedagogically meaningful than synthetic augmentations. Experiments on four benchmarks demonstrate that RACL achieves +1.2% average AUC improvement over state-of-the-art methods, with 97% performance retention at 20% training data, indicating improved robustness under sparse-learning conditions.

Graph anomaly detection identifies abnormal patterns in networks but faces label scarcity and extreme class imbalance. While graph contrastive learning offers unsupervised solutions, existing methods suffer from two limitations: random augmentations break semantic consistency in positive pairs, while naive negative sampling produces trivial contrasts. We propose AC2L-GAD, an Active Counterfactual Contrastive Learning framework addressing both limitations through principled counterfactual reasoning. By combining information-theoretic active selection with counterfactual generation, our approach identifies structurally complex nodes and generates anomaly-preserving positive augmentations alongside hard negative contrasts, while restricting expensive counterfactual generation to a strategically selected subset. This design reduces computational overhead by approximately 65% compared to full-graph counterfactual generation while maintaining detection quality. Experiments on nine benchmark datasets, including real-world financial transaction graphs from GADBench, show that AC2L-GAD achieves competitive or superior performance compared to state-of-the-art baselines, with notable gains in datasets where anomalies exhibit complex attribute-structure interactions.

Attributed graph clustering is crucial for analyzing complex networks, but integrating heterogeneous structural and attribute information remains a challenging task. Existing methods often struggle to balance these aspects, resulting in suboptimal clustering performance. To address this, we propose DV-ERNMF (Dual-View Entropy Regularized Nonnegative Matrix Factorization), a framework that decomposes the attributed network into two complementary views, structure and attributes, for separate, yet coordinated modeling. In the structural view, we introduce a Symmetric Nonnegative Matrix Factorization (SNMF) model enhanced with entropy-based regularization to yield sharper cluster assignments. For the attribute view, we construct a clustering-specific similarity matrix via subspace learning and apply SNMF to extract a structurally consistent cluster pattern. A new adaptive entropy-based regularizer is applied to enforce consistency between the partitions obtained from both views. The entire model is optimized jointly using a multiplicative update rule with theoretical convergence guarantees. Experimental results on synthetic and real-world networks demonstrate that DV-ERNMF significantly outperforms state-of-the-art methods.

Attributed graph clustering is a fundamental task in network mining, essential for uncovering valuable insights in various applications. However, the heterogeneity of information from structural and attribute spaces poses significant challenges in achieving consistent and meaningful clustering. To address this, we propose Relative Entropy-based Regularized Non-negative Matrix Factorization (RENMF), a novel approach that integrates structural and attribute information through advanced matrix factorization techniques. RENMF employs Symmetric NMF and Projective NMF to extract community membership distributions from the structural and attribute spaces, respectively. By treating these distributions as homogeneous, RENMF preserves distinct, denoised information from both spaces while considering their heterogeneous complementary information. We introduce Relative Entropy (RE) as a novel regularization term to facilitate interaction between these spaces, aiming to maximize consistency between the discovered latent distributions. In this interaction, we leverage the asymmetric property of RE to emphasize attributes as essential complementary information for structural clustering. The RENMF model is solved using a new iterative multiplicative update rule, with convergence theoretically proven. We evaluate RENMF’s effectiveness through extensive experiments on 10 real-world networks, comparing it to 11 state-of-the-art clustering methods. The results demonstrate RENMF’s superiority in ground truth matching and key quality metrics, outperforming existing methods.