Graph Signal Research Articles

Decomposing cortical activity through neuronal tracing connectome-eigenmodes in marmosets

Deciphering the complex relationship between neuroanatomical connections and functional activity in primate brains remains a daunting task, especially regarding the influence of monosynaptic connectivity on cortical activity. Here, we investigate the anatomical-functional relationship and decompose the neuronal-tracing connectome of marmoset brains into a series of eigenmodes using graph signal processing. These cellular connectome eigenmodes effectively constrain the cortical activity derived from resting-state functional MRI, and uncover a patterned cellular-functional decoupling. This pattern reveals a spatial gradient from coupled dorsal-posterior to decoupled ventral-anterior cortices, and recapitulates micro-structural profiles and macro-scale hierarchical cortical organization. Notably, these marmoset-derived eigenmodes may facilitate the inference of spontaneous cortical activity and functional connectivity of homologous areas in humans, highlighting the potential generalizing of the connectomic constraints across species. Collectively, our findings illuminate how neuronal-tracing connectome eigenmodes constrain cortical activity and improve our understanding of the brain’s anatomical-functional relationship.

Discrepant changes in structure-function coupling in dancers and musicians.

Dance and music are well known to improve sensorimotor skills and cognitive functions. To reveal the underlying mechanism, previous studies focus on the brain plastic structural and functional effects of dance and music training. However, the discrepancy training effects on brain structure-function relationship are still blurred. Thus, proficient dancers, musicians, and controls were recruited in this study. The graph signal processing framework was employed to quantify the region-level and network-level relationship between brain function and structure. The results showed the increased coupling strength of the right ventromedial putamen in the dance and music groups. Distinctly, enhanced coupling strength of the ventral attention network, increased coupling strength of the right inferior frontal gyrus opercular area, and increased function connectivity of coupling function signal between the right and left middle frontal gyrus were only found in the dance group. Besides, the dance group indicated enhanced coupling function connectivity between the left inferior parietal lobule caudal area and the left superior parietal lobule intraparietal area compared with the music groups. The results might illustrate dance and music training's discrepant effect on the structure-function relationship of the subcortical and cortical attention networks. Furthermore, dance training seemed to have a greater impact on these networks.

Graph signal reconstruction based on spatio-temporal features learning

This paper presents a new algorithm for reconstructing time-varying graph signals using spatiotemporal feature learning. We introduce a time series analysis method to capture the temporal stationarity of graph signals and propose a reconstruction model based on spatiotemporal coupling features. However, prior knowledge of the temporal stationarity of graph signals is required for this task. To address the issue, we analyze the spatio-temporal coupling feature in a graph-spectral view and design a learning framework to capture only the temporal feature based on the sampled signals. We reconstruct the graph signals using the proposed reconstruction model and feature-learning framework by solving an unconstrained optimization problem consisting of data fidelity and two regularization terms. Numerical results using both synthetic and real-world datasets demonstrate the superiority of the proposed reconstruction algorithm over existing methods.

Utilizing Graph Signal-Processing-Based Spectrum to Classify Mental Tasks With Multichannel EEG Signals

Utilizing Graph Signal-Processing-Based Spectrum to Classify Mental Tasks With Multichannel EEG Signals

Graph signal recovery using variational Bayes in Fourier pairs with Cramér–Rao bounds

In this paper, the graph signal recovery problem is addressed by employing an aggregation of samples in the vertex domain and the Fourier graph transform domain. The statistical graph signal is modeled using a Gaussian Markov Random Field (GMRF). The reconstruction process involves employing a variational Bayes (VB) algorithm, which is a fully Bayesian method that iteratively estimates all unknown parameters by computing the posteriors in a closed-form. Furthermore, the closed-form of the Cramér–Rao lower bound (CRLB) for graph signal estimation is also derived. Simulation results demonstrate the superiority of the proposed algorithm over some of state-of-the-art algorithms in the literature.

An interpretable model based on graph learning for diagnosis of Parkinson’s disease with voice-related EEG

Parkinson’s disease (PD) exhibits significant clinical heterogeneity, presenting challenges in the identification of reliable electroencephalogram (EEG) biomarkers. Machine learning techniques have been integrated with resting-state EEG for PD diagnosis, but their practicality is constrained by the interpretable features and the stochastic nature of resting-state EEG. The present study proposes a novel and interpretable deep learning model, graph signal processing-graph convolutional networks (GSP-GCNs), using event-related EEG data obtained from a specific task involving vocal pitch regulation for PD diagnosis. By incorporating both local and global information from single-hop and multi-hop networks, our proposed GSP-GCNs models achieved an averaged classification accuracy of 90.2%, exhibiting a significant improvement of 9.5% over other deep learning models. Moreover, the interpretability analysis revealed discriminative distributions of large-scale EEG networks and topographic map of microstate MS5 learned by our models, primarily located in the left ventral premotor cortex, superior temporal gyrus, and Broca’s area that are implicated in PD-related speech disorders, reflecting our GSP-GCN models’ ability to provide interpretable insights identifying distinctive EEG biomarkers from large-scale networks. These findings demonstrate the potential of interpretable deep learning models coupled with voice-related EEG signals for distinguishing PD patients from healthy controls with accuracy and elucidating the underlying neurobiological mechanisms.

Verifying the Smoothness of Graph Signals: A Graph Signal Processing Approach

Verifying the Smoothness of Graph Signals: A Graph Signal Processing Approach

Modeling Sparse Graph Sequences and Signals Using Generalized Graphons

Modeling Sparse Graph Sequences and Signals Using Generalized Graphons

Random Sampling of Bandlimited Graph Signals From Local Measurements

Random Sampling of Bandlimited Graph Signals From Local Measurements

Kernel Based Reconstruction for Generalized Graph Signal Processing

Kernel Based Reconstruction for Generalized Graph Signal Processing

Filter-Informed Spectral Graph Wavelet Networks for Multiscale Feature Extraction and Intelligent Fault Diagnosis.

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use of the inductive bias of the interdependencies between the different sensor measurements. However, there are some limitations with these GNN-based fault diagnosis methods. First, they lack the ability to realize multiscale feature extraction due to the fixed receptive field of GNNs. Second, they eventually encounter the over-smoothing problem with increase of model depth. Finally, the extracted features of these GNNs are hard to understand due to the black-box nature of GNNs. To address these issues, a filter-informed spectral graph wavelet network (SGWN) is proposed in this article. In SGWN, the spectral graph wavelet convolutional (SGWConv) layer is established upon the spectral graph wavelet transform, which can decompose a graph signal into scaling function coefficients and spectral graph wavelet coefficients. With the help of SGWConv, SGWN is able to prevent the over-smoothing problem caused by long-range low-pass filtering, by simultaneously extracting low-pass and band-pass features. Furthermore, to speed up the computation of SGWN, the scaling kernel function and graph wavelet kernel function in SGWConv are approximated by the Chebyshev polynomials. The effectiveness of the proposed SGWN is evaluated on the collected solenoid valve dataset and aero-engine intershaft bearing dataset. The experimental results show that SGWN can outperform the comparative methods in both diagnostic accuracy and the ability to prevent over-smoothing. Moreover, its extracted features are also interpretable with domain knowledge.

Voxel-Wise Brain Graphs From Diffusion MRI: Intrinsic Eigenspace Dimensionality and Application to Functional MRI

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Goal:</i> Structural brain graphs are conventionally limited to defining nodes as gray matter regions from an atlas, with edges reflecting the density of axonal projections between pairs of nodes. Here we explicitly model the entire set of voxels within a brain mask as nodes of high-resolution, subject-specific graphs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> We define the strength of local voxel-to-voxel connections using diffusion tensors and orientation distribution functions derived from diffusion MRI data. We study the graphs' Laplacian spectral properties on data from the Human Connectome Project. We then assess the extent of inter-subject variability of the Laplacian eigenmodes via a procrustes validation scheme. Finally, we demonstrate the extent to which functional MRI data are shaped by the underlying anatomical structure via graph signal processing. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> The graph Laplacian eigenmodes manifest highly resolved spatial profiles, reflecting distributed patterns that correspond to major white matter pathways. We show that the intrinsic dimensionality of the eigenspace of such high-resolution graphs is only a mere fraction of the graph dimensions. By projecting task and resting-state data on low-frequency graph Laplacian eigenmodes, we show that brain activity can be well approximated by a small subset of low-frequency components. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusions:</i> The proposed graphs open new avenues in studying the brain, be it, by exploring their organisational properties via graph or spectral graph theory, or by treating them as the scaffold on which brain function is observed at the individual level.

Behavior analysis for trajectory graph signal using graph wavelet transform

Behavior analysis for trajectory graph signal using graph wavelet transform

Detecting Low Pass Graph Signals via Spectral Pattern: Sampling Complexity and Applications

Detecting Low Pass Graph Signals via Spectral Pattern: Sampling Complexity and Applications

A New Approach for Graph Signal Separation Based on Smoothness

A New Approach for Graph Signal Separation Based on Smoothness

Integrating Graph Signal Processing and Multitask Temporal Convolutional Networks for Household Nonintrusive Load Monitoring

Integrating Graph Signal Processing and Multitask Temporal Convolutional Networks for Household Nonintrusive Load Monitoring

Online Signed Sampling of Bandlimited Graph Signals

Online Signed Sampling of Bandlimited Graph Signals

Graph Signal Reconstruction Under Heterogeneous Noise via Adaptive Uncertainty-Aware Sampling and Soft Classification

Graph Signal Reconstruction Under Heterogeneous Noise via Adaptive Uncertainty-Aware Sampling and Soft Classification

Graph Multi-Scale Permutation Entropy for Bearing Fault Diagnosis.

Bearing faults are one kind of primary failure in rotatory machines. To avoid economic loss and casualties, it is important to diagnose bearing faults accurately. Vibration-based monitoring technology is widely used to detect bearing faults. Graph signal processing methods promising for the extraction of the fault features of bearings. In this work, graph multi-scale permutation entropy (MPEG) is proposed for bearing fault diagnosis. In the proposed method, the vibration signal is first transformed into a visibility graph. Secondly, a graph coarsening method is used to generate coarse graphs with different reduced sizes. Thirdly, the graph's permutation entropy is calculated to obtain bearing fault features. Finally, a support vector machine (SVM) is applied for fault feature classification. To verify the effectiveness of the proposed method, open-source and laboratory data are used to compare conventional entropies and other graph entropies. Experimental results show that the proposed method has higher accuracy and better robustness and de-noising ability.

Robust logarithmic hyperbolic cosine adaptive filtering over graph signals

Graph signal processing (GSP) has two methods including graph Fourier transform (GFT) and graph shift-operator (GSO) for dealing with the graph signal used for adaptive filtering (AF). However, in order to perform feature decomposition, GFT requires the availability of a band-limited graph signal with a known bandwidth in advance. Therefore, a general model based on GSO is then derived for AF by introducing a mixture coefficient to combine the advantages of different GSOs, comprehensively. Since the existing algorithms using the mean square error and other robust error criteria in GSP cannot effectively fight against non-Gaussian noises, a robust logarithmic hyperbolic cosine adaptive filter over graph (GLHCAF) algorithm is proposed by applying the logarithmic hyperbolic cosine loss function to the designed general model. The significant performance improvement of GLHCAF in non-Gaussian noises is obtained by simply controlling the scaling parameter. To avoid the parameter selections including scaling parameter and step size, the adaptive GLHCAF (AGLHCAF) algorithm is therefore proposed to further improve the performance of GLHCAF. Moreover, the mean square performance analysis of GLHCAF is given. Simulations in the real-world data are provided to assess the reliability and accuracy for theoretical analysis, the universality of the designed general model, and superiorities of proposed algorithms.