Guest Editorial: Graph Representation Learning for Feature Extraction and Signal Processing

In recent years, graph representation learning has evolved from a highly specialised theoretical mathematical concept into a widely used foundational method across artificial intelligence, feature extraction and signal processing. As our digital data grows, real-world data across various critical domains—ranging from the complex topologies of smart power grids and intelligent transportation networks to the large-scale dynamic architectures of complex cyber-physical systems—can be naturally and effectively modelled as non-Euclidean graph structures. Traditional signal processing and feature extraction techniques, which were primarily designed for grid-like data, such as images or time-series, often are insufficient when capturing the complex irregular relational dependencies found in these modern systems. Consequently, extracting meaningful, robust features and processing signals efficiently from these high-dimensional networks presents both a major challenge and a great opportunity. Researchers are tasked with overcoming significant obstacles, including scalability limits, vulnerability to topological noise and the difficulty of modelling spatiotemporal dynamics. This special issue, ‘Graph Representation Learning for Feature Extraction and Signal Processing’, is dedicated to showcasing the latest theoretical breakthroughs and innovative, practical applications in this rapidly expanding field. Following a strict and highly competitive peer-review process, we are proud to present four outstanding papers that reflect the true breadth, depth and advanced direction of current research. The first paper, ‘Enhancing generalised spectral clustering with embedding Laplacian graph regularisation’ by Hengmin Zhang et al., addresses critical long-standing challenges in unsupervised learning and feature extraction. Although traditional spectral clustering is a powerful tool, it often lacks stability when dealing with noisy data or overlapping clusters. The authors effectively solve this by proposing a generalised spectral clustering framework that structurally integrates a Laplacian graph and a ‘group effect’ into a highly flexible regularisation term. This new unified approach significantly improves the algorithm's discriminative power, allowing it to keep high accuracy even under highly noisy conditions. Furthermore, the study overcomes traditional computational limitations by introducing an efficient optimisation algorithm utilising the standard Sylvester equation, alongside an alternating iterative re-weighted process (AIwRP). This ensures that the model maintains excellent computational efficiency without sacrificing the mathematical correctness or accuracy of the clustering outcomes. The second paper, ‘Short-Term Multi-Horizon Line Loss Rate Forecasting of a Distribution Network Using Attention-GCN-LSTM’ by Jie Liu et al., presents a highly practical and important application of graph neural networks within the field of smart grid signal processing. Accurately forecasting line loss rates across multiple time horizons—ranging from 1 hour up to a full week—is absolutely necessary for modern power supply management, energy conservation and carbon footprint reduction. However, distribution networks are highly changeable, with complex spatial topologies and highly variable temporal load signals. To handle this complexity, the authors developed the attention–GCN–LSTM model. This architecture combines graph convolutional networks (GCNs) to map the spatial topology of distribution nodes with long short-term memory (LSTM) networks to analyse historical temporal dependencies. Importantly, the integration of an advanced three-level attention mechanism allows the model to dynamically evaluate the importance of different nodes and features. Evaluated against real-world data from 10 kV feeders, this integrated approach demonstrated a strong ability to consistently outperform existing baseline algorithms across multiple forecasting horizons. The third paper, ‘Generating Compressed Counterfactual Hard Negative Samples for Graph Contrastive Learning’ by Haoran Yang et al., investigates the underlying mechanics of self-supervised learning, addressing a fundamental limitation: the ‘false negative’ sampling problem. Graph contrastive learning (GCL) heavily relies on contrasting positive samples against negative ones to learn rich structural semantics. However, randomly sampling negative graphs often results in selecting ‘false negatives’—graphs that are actually semantically identical to the target, which heavily decreases model training quality. The researchers introduce an innovative method called CGC, which effectively uses a counterfactual mechanism to intentionally generate high-quality ‘hard’ negative samples. These generated samples are structurally highly similar to the original graph but essentially different in their semantic labels. Recognising that generating and storing these augmented graphs introduces severe space complexity issues, the authors advance the research further by proposing CCGC. This extension incorporates a teacher-free knowledge distillation compression module, efficiently minimising feature storage requirements whilst actually improving the overall performance of the contrastive learning framework. The fourth paper, ‘Graph neural network-based attack prediction for communication-based train control systems’ by Junyi Zhao et al., explores the critical connection between graph learning algorithms and industrial cybersecurity. As critical infrastructure becomes increasingly digitised, communication-based train control (CBTC) systems have become main targets for highly complex advanced persistent threats (APTs). The study proposes the GNN–AP framework, a strong defencive mechanism designed to predict and outline multistep cyberattacks. Moving beyond simple anomaly detection, the framework utilises causal relationships to filter noisy system alert logs and uses an encoder–decoder model to comprehensively reconstruct an attack scenario graph. By aligning these multistep attack sequences with the underlying topological map of the CBTC network, the framework uses a graph neural network to infer the attacker's hidden intent. By effectively formulating the prediction of future attack targets as a link-prediction problem within the graph, the GNN–AP model offers a powerful proactive tool for protecting critical transit infrastructure. Together, these four articles highlight the broad adaptability and strong computational power of graph representation learning. Whether researchers are optimising the foundational mathematics of clustering algorithms, advancing the limits of self-supervised contrastive learning or solving urgent specific industry challenges in power distribution and rail transit security, the methodologies presented here offer highly valuable insights. They demonstrate that when we learn to properly model the relationships between data points rather than just the data points themselves, we open a new method of intelligent signal processing. We extend our sincere thanks to all the contributing authors who shared their excellent rigorous work with this special issue. We are equally grateful to the anonymous reviewers whose detailed feedback and constructive critiques ensured the highest standards of scientific excellence. Finally, we thank the editorial board for their continuous support throughout the publication process. We hope this carefully selected collection inspires our readers, encourages cross-disciplinary collaboration and stimulates further significant advancements in the interesting and growing domain of graph representation learning. We gratefully acknowledge the contributions of our fellow guest editors: Xiao Bai, Jun Zhou, Hongzhi Yin, Lusi Li and Edwin R. Hancock to this special section. Data sharing is not applicable to this article as no new data were created or analysed in this study. Xin Ning (Senior Member, IEEE) received the B.S. degree in software engineering from Xinjiang University in 2012, and the Ph.D. degree in computer vision from university of Chinese Academy of Sciences, in 2017. He is currently a Professor with the Institute of Semiconductors, Chinese Academy of Sciences. His current research interests include neural networks, intelligent systems and computer vision. His Google Scholar total citation reached 8000+, with an H-index of 50. He has been featured in the list of top 2% scientist/researcher databases in the world in 2022–2025. He has published by first or corresponding author more than 80 papers in journals and refereed conferences. He served as a senior member of IEEE/CCF/CAAI/CSIG. He is working as Guest Editor, Associate Editor in SCI and various other reputed journals (IEEE, Elsevier, Springer). He serves as Aare Editor in the Information Fusion and Associate Editor in the IEEE TCSVT, Pattern Recognition, Applied Soft Computing, Engineering Applications of Artificial Intelligence and Signal Processing journal. And he also serves as the Young Associate Editor of CAAI Transactions on Intelligent Systems, the Guest Editor of IEEE TCE, Image and Vision Computing et al. He was the Website Chair of the IEEE HPBD&IS 2020, and the Publication Chair of the IEEE HPBD&IS 2021, HDIS 2022 and HDIS 2023.