Temporal Betweenness Centrality (TBC) measures how often a node appears on optimal temporal paths, reflecting its importance in temporal networks. However, exact computation is highly expensive, and real-world TBC distributions are extremely imbalanced, causing learning-based models to overfit to zero-centrality nodes and fail to identify truly central nodes. Existing graph neural networks (GNNs) either ignore temporal dependencies or cannot handle such extreme imbalance. To address these issues, we propose CLGNN, a scalable and inductive contrastive learning-based GNN for accurate TBC prediction. CLGNN preserves temporal path validity through an instance graph and encodes structural, path-time aware dependencies via dual aggregation. To mitigate imbalance, a stability-based clustering-guided contrastive module separates nodes of different centrality levels in representation space, while a regression head estimates TBC values. Extensive experiments on diverse benchmarks demonstrate that CLGNN is scalable, generalizable, and effective.

As climate change intensifies, the electricity industry is crucial for achieving carbon neutrality, but carbon price volatility makes prediction challenging. Traditional statistical and econometric models struggle to capture the nonlinear features of carbon prices effectively. In recent years, deep learning methods, particularly Graph Neural Networks (GNNs), have made significant progress in modeling spatial and temporal dependencies. However, traditional GNNs face limitations in handling higher-order relationships and temporal dependencies among multiple entities. This paper proposes CPP-GNN, a carbon price prediction model based on Temporal Hypergraph Graph Neural Networks. The core innovation lies in using a hypergraph structure to represent complex relationships and employing temporal GNNs to capture the dynamic evolution of carbon prices. Experimental results demonstrate that CPP-GNN performs excellently across multiple carbon emission trading datasets from different regions, significantly outperforming the best benchmark models. CPP-GNN consistently outperforms baselines, achieving an average improvement of 9.3% in mean absolute error, 7.5% in root mean squared error, and 2.6% in directional accuracy. Notably, the model achieves the largest gains in highly dynamic markets such as GDEA and SHEA, highlighting its robustness and adaptability. Therefore, decisionmaking in the electricity market can be further supported by CPP-GNN.

Accurate modeling of structured spatio-temporal signals remains challenging due to complex spatial, temporal, and frequency-domain dependencies. Existing graph neural networks (GNNs) typically neglect frequency-domain anomalies and multi-scale temporal dynamics. To address these gaps, we propose STSSRI-GNN, a Spatio-Temporal Graph Neural Network integrating multi-scale temporal convolution, spectral-aware encoding, and dynamic message passing. Experiments on smart grid, industrial anomaly detection, and biomedical datasets show STSSRI-GNN significantly outperforms state-of-the-art models. Specifically, STSSRI-GNN achieves up to 27.2% lower forecasting MAE, 11% higher anomaly detection PR-AUC, and 5.6% improvement in ECG classification F1-score. Ablation studies further validate the critical role of temporal encoding, attention mechanisms, and spectral-aware features, highlighting the model’s robust generalization across diverse structured signal domains.

Accurate and efficient operational risk prediction is critical for modern power systems facing dynamic unit commitment and renewable integration. Existing machine learning and deep learning approaches often ignore grid topology or temporal evolution, limiting their ability to capture fault propagation under evolving system states. We propose TGN-RiBC, a Betweenness-Aware Temporal Graph Neural Network that incorporates temporal attention, temporal betweenness centrality (TBC), and contrastive learning to jointly model temporal dynamics and structural vulnerability. TGN-RiBC uses time-aware message passing and reachability-based supervision to identify propagation-critical nodes in real time. Experiments on three benchmark systems demonstrate that TGN-RiBC reduces prediction error by up to 3 times compared to classical models and achieves 1.5 to 2 times lower error than prior GNNs, while delivering 60 to 117 times faster inference than SCUC solvers. It maintains reliability with load shedding deviation under 3%, remains robust under up to 20% hourly generator changes, and ablation studies confirm that all core components—temporal encoding, centrality-aware attention, and contrastive learning—are essential to its performance.

As one of the most effective feature learning methods, Nonnegative Matrix Factorization (NMF) has been widely used in many scientific fields, such as computer vision, data mining, and bioinformatics. However, NMF is an unsupervised method that cannot fully utilize the label information of data. Thus, its performance is limited in some recognition and classification problems. To remedy this shortcoming, this paper proposes a Semisupervised Discriminative NMF (SDNMF) method. First, we design a Soft-Labeled NMF (SLNMF) model by introducing a soft-label matrix-based regression term into the original NMF, so that the relationship between the soft-label matrix and low-dimensional features can be constructed to improve the discriminative ability of low-dimensional features. Second, to effectively estimate the soft-label matrix, a Label Propagation (LP) model is adopted to fully explore the spatial distribution relationship between the labeled and unlabeled samples. Third, an Adaptive Graph Learning (AGL) model is proposed to exploit the geometric relationship of samples well, which could enhance the performance of LP. Finally, the above three models (i.e., SLNMF, LP, and AGL) are integrated into a unified framework for effective feature learning, which can not only effectively explore the structural relationship matrix between data, but also predict the labels for unknown samples. Moreover, an iterative optimization algorithm is presented to solve our objective function. The convergence and computational complexity analysis of the proposed SDNMF method are also provided. Extensive experiments are conducted on several standard data sets. Compared with related methods, the experimental results verify that the proposed SDNMF method achieves better performance.