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•The relation of brain function with the underlying structural wiring is complex.•We propose new structure-informed graph signal processing (GSP) filtering of functional data.•GSP-derived features allow accurate task decoding and individual fingerprinting.•Functional connectivity from filtered data is more unique to subject and cognition.•The role of structurally aligned and liberal graph frequencies is elucidated. Brain signatures of functional activity have shown promising results in both decoding brain states, meaning distinguishing between different tasks, and fingerprinting, that is identifying individuals within a large group. Importantly, these brain signatures do not account for the underlying brain anatomy on which brain function takes place. Structure-function coupling based on graph signal processing (GSP) has recently revealed a meaningful spatial gradient from unimodal to transmodal regions, on average in healthy subjects during resting-state. Here, we explore the specificity of structure-function coupling to distinct brain states (tasks) and to individual subjects. We used multimodal magnetic resonance imaging of 100 unrelated healthy subjects from the Human Connectome Project both during rest and seven different tasks and adopted a support vector machine classification approach for both decoding and fingerprinting, with various cross-validation settings. We found that structure-function coupling measures allow accurate classifications for both task decoding and fingerprinting. In particular, key information for fingerprinting is found in the more liberal portion of functional signals, with contributions strikingly localized to the fronto-parietal network. Moreover, the liberal portion of functional signals showed a strong correlation with cognitive traits, assessed with partial least square analysis, corroborating its relevance for fingerprinting. By introducing a new perspective on GSP-based signal filtering and FC decomposition, these results show that brain structure-function coupling provides a new class of signatures of cognition and individual brain organization at rest and during tasks. Further, they provide insights on clarifying the role of low and high spatial frequencies of the structural connectome, leading to new understanding of where key structure-function information for characterizing individuals can be found across the structural connectome graph spectrum.

The Normalized Difference Vegetation Index (NDVI) is a crucial remote-sensing metric for assessing land surface vegetation greenness, essential for various studies encompassing phenology, ecology, hydrology, etc. However, effective applications of NDVI data are hindered by data noise due to factors such as cloud contamination, posing challenges for accurate observation. In this study, we proposed a novel approach for employing a Temporal-Difference Graph (TDG) method to reconstruct low-quality pixels in NDVI data. Regarding spatio-temporal NDVI data as a time-varying graph signal, the developed method utilized an optimization algorithm to maximize the spatial smoothness of temporal differences while preserving the spatial NDVI pattern. This approach was further evaluated by reconstructing MODIS/Terra Vegetation Indices 16-Day L3 Global 250 m Grid (MOD13Q1) products over Northwest China. Through quantitative comparison with a previous state-of-the-art method, the Savitzky–Golay (SG) filter method, the obtained results demonstrated the superior performance of the TDG method, and highly accurate results were achieved in both the temporal and spatial domains irrespective of noise types (positively-biased, negatively-biased, or linearly-interpolated noise). In addition, the TDG-based optimization approach shows great robustness to noise intensity within spatio-temporal NDVI data, suggesting promising prospects for its application to similar datasets.

Learning graph structure from observed signals over graph is a crucial task in many graph signal processing (GSP) applications. Existing approaches focus on inferring static graph, typically assuming that all nodes are available. However, these approaches ignore the situation where only a subset of nodes are available from spatiotemporal measurements, and the remaining nodes are never observed due to application-specific constraints, resulting in time-varying graph estimation accuracy declines dramatically. To handle this problem, we propose a framework that consider the presence of hidden nodes to identify time-varying graph. Specifically, we assume that the graph signals are smooth and stationary on the graphs and only a small number of edges are allowed to change between two consecutive graphs. With these assumptions, we present a challenging time-varying graph inference problem, which models the influence of hidden nodes in terms of estimating the graph-shift operator matrices that have a form of graph Laplacian. Moreover, we emphasize similar edge pattern (column-sparsity) between different graphs. Finally, our method is evaluated on both synthetic and real-world data. The experimental results demonstrate the advantage of our method when compared to existing benchmarking methods.

This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.

[This corrects the article DOI: 10.3389/fnins.2025.1608739.].

In this paper, we introduce an Adaptive Graph Signal Processing with Dynamic Semantic Alignment (AGSP-DSA) framework to perform robust multimodal data fusion across heterogeneous sources, including text, audio, and images. The proposed approach uses a dual-graph construction to learn both intra-model and inter-modal relations, spectral graph filtering to enhance informative signals, and effective node embeddings via Multi-scale Graph Convolutional Networks. In the semantic-aware attention mechanism, each modality may dynamically contribute to the context with respect to contextual relevance. The experimental outcomes on three benchmark datasets, including Carnegie Mellon University Multimodal Opinion Sentiment and Emotion Intensity dataset, Audio-Visual Event dataset, and MultiModal Internet Movie Database dataset, show that Adaptive Graph Signal Processing with Dynamic Semantic Alignment performs as the state of the art. More precisely, it achieves 95.3% accuracy, 93.6% F1 (Harmonic Mean of Precision and Recall) score, and 92.4% mean average precision on the Carnegie Mellon University Multimodal Opinion Sentiment and Emotion Intensity dataset, improving the MultiModal Graph Neural Network by 2.6% in accuracy. It gets 93.4% accuracy and 91.1% F1 score on Audio-Visual Event dataset, and 91.8% accuracy and 88.6% F1 score on MultiModal Internet Movie Database dataset, which demonstrates good generalization and robustness in the missing modality setting. These findings verify the efficiency of the proposed AGSP-DSA in promoting multimodal learning in sentiment analysis, event recognition, and multimedia classification.

Autism spectrum disorder (ASD) is a complex neurodevelopmental condition associated with disrupted brain connectivity. Traditional graph-theoretical approaches have been widely employed to study ASD biomarkers; however, these methods are often limited to static topological measures and lack the capacity to capture spectral characteristics of brain activity, especially in multimodal data settings. This limits their ability to model dynamic neural interactions and reduces their diagnostic precision. To overcome these limitations, we propose a Graph Signal Processing (GSP)-based framework that integrates spectral-domain features with topological descriptors to model brain connectivity more comprehensively. Using publicly available fMRI and EEG datasets, we construct subject-specific connectivity graphs where nodes represent brain regions and edges encode functional interactions. We extract advanced GSP features such as Graph Fourier Transform coefficients, spectral entropy, and clustering coefficients, and combine them using Principal Component Analysis (PCA). These are classified using a Support Vector Machine (SVM) with a radial basis function (RBF) kernel. The proposed model achieves 98.8% classification accuracy, significantly outperforming prior multimodal GSP studies. Feature ablation analysis reveals that spectral entropy contributes most to this improvement, with its removal resulting in a nearly 30% performance drop. Additionally, a 25% sparsity threshold in graph construction was found to maximize both robustness and computational efficiency. These findings demonstrate that incorporating frequency-domain information through GSP enables a more discriminative and biologically meaningful representation of ASD-related neural patterns, offering a promising direction for accurate diagnosis and biomarker discovery.

With the advancement of brain imaging techniques and a variety of machine learning methods, significant progress has been made in brain disorder diagnosis, in particular Autism Spectrum Disorder. The development of machine learning models that can differentiate between healthy subjects and patients is of great importance. Recently, graph neural networks have found increasing application in domains where the population’s structure is modeled as a graph. The application of graphs for analyzing brain imaging datasets helps to discover clusters of individuals with a specific diagnosis. However, the choice of the appropriate population graph becomes a challenge in practice, as no systematic way exists for defining it. To solve this problem, we propose a population graph-based multi-model ensemble, which improves the prediction, regardless of the choice of the underlying graph. First, we construct a set of population graphs using different combinations of imaging and phenotypic features and evaluate them using Graph Signal Processing tools. Subsequently, we utilize a neural network architecture to combine multiple graph-based models. The results demonstrate that the proposed model outperforms the state-of-the-art methods on Autism Brain Imaging Data Exchange (ABIDE) dataset.

Accurate assessment of winding faults in large power autotransformers using frequency response analysis (FRA) remains challenging due to the complex electromechanical coupling between winding geometry and the measured response. This paper proposes a graph-based diagnostic framework that links physics-based FRA modeling with probabilistic machine learning for fault type identification, localization, and severity estimation. First, a RLC state-space model of a 125 MVA, 230/132/20 kV power autotransformer is developed and validated against measured FRA traces in the healthy state. Subsequently, simulation-based faulty FRA datasets are then generated by applying mechanical deformations, including axial displacement (AD) and radial deformation (RD), and an electrical turn-to-turn short-circuit (TTSC) fault through corresponding geometry/parameter variations. Each FRA trace is converted into a graph representation using the weighted visibility-graph approach, and informative features are extracted from the resulting graph-domain spectrum. A Gaussian-process (GP) pipeline is subsequently employed, where Type-GPC performs multi-class fault type identification (Healthy/AD/RD/TTSC), Location-GPC localizes TTSC faults, and fault-specific GPR models estimate severity with quantified uncertainty. Experimental results show overall accuracies of 92.9 % for fault type identification and 92.0 % for TTSC localization. Severity estimation achieves MAE/RMSE of 1.00 %/1.34 % for AD/RD and 5.30  /5.91  for TTSC, demonstrating reliable and interpretable diagnostics.

Hyperspectral imaging has broad applications and impacts in areas including environmental science, weather, and geo/space exploration. The intrinsic spectral–spatial structures and potential multi-level features in different frequency bands make multilayer graph an intuitive model for hyperspectral images (HSI). To study the underlying characteristics of HSI and to take the advantage of graph signal processing (GSP) tools, this work proposes a multilayer graph spectral analysis for hyperspectral images based on multilayer graph signal processing (M-GSP). More specifically, we present multilayer graph (MLG) models and tensor representations for HSI. By exploring multilayer graph spectral space, we develop MLG-based methods for HSI applications, including unsupervised segmentation and supervised classification. Our experimental results demonstrate the strength of M-GSP in HSI processing and spectral–spatial information extraction.