Adjacency Matrix Research Articles

Structural and Spectral Properties of Chordal Ring, Multi-Ring, and Mixed Graphs

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), chordal ring mixed (CRM), and chordal multi-ring mixed (CMRM) graphs. In the case of mixed graphs, we can have edges (without direction) and arcs (with direction). The chordal ring and chordal ring mixed graphs are bipartite and 3-regular. They consist of a number r (for r≥1) of (undirected or directed) cycles with some edges (the chords) joining them. In particular, for CMR, when r=1, that is, with only one undirected cycle, we obtain the known families of chordal ring graphs. Here, we used plane tessellations to represent our chordal multi-ring graphs. This allowed us to obtain their maximum number of vertices for every given diameter. Additionally, we computationally obtained their minimum diameter for any value of the number of vertices. Moreover, when seen as a lift graph (also called voltage graph) of a base graph on Abelian groups, we obtained closed formulas for the spectrum, that is, the eigenvalue multi-set of its adjacency matrix.

Synchronization processes in fNIRS visibility networks

We employ Kuramoto model to assess the presence of synchronization in individuals who fulfill a cooperation task. Our input data is a couple of signals obtained from functional Near-Infrared Spectroscopy Data Acquisition and Pre-processing technology that is used to capture the brain activity of an individual by measuring the oxyhemoglobin (HbO) level. We consider 1 min signal for individuals in three distinct states: (i) rest; (ii) before a disturb happens; (iii) after the disturbance. We estimate global and local order parameters synchronization with the purpose to compare the conditions of reaching a synchronous state in the networks corresponding to different states for distinct individuals and hemispheres of the prefrontal cortices of same individual. Experimental results confirmed once more that coherent state is reached not for same conditions in both individuals and hemispheres of the prefrontal cortices. Furthermore, condition changes even for different events. The computation of the effective frequencies for each degree class indicates clearly the network difference in rest, before and after disturb. Finally, we investigate the dynamic connectivity matrix and consider the similarity between distinct prefrontal cortices over time.

Multi-Domain Based Dynamic Graph Representation Learning for EEG Emotion Recognition.

Graph neural networks (GNNs) have demonstrated efficient processing of graph-structured data, making them a promising method for electroencephalogram (EEG) emotion recognition. However, due to dynamic functional connectivity and nonlinear relationships between brain regions, representing EEG as graph data remains a great challenge. To solve this problem, we proposed a multi-domain based graph representation learning (MD 2GRL) framework to model EEG signals as graph data. Specifically, MD 2GRL leverages gated recurrent units (GRU) and power spectral density (PSD) to construct node features of two subgraphs. Subsequently, the self-attention mechanism is adopted to learn the similarity matrix between nodes and fuse it with the intrinsic spatial matrix of EEG to compute the corresponding adjacency matrix. In addition, we introduced a learnable soft thresholding operator to sparsify the adjacency matrix to reduce noise in the graph structure. In the downstream task, we designed a dual-branch GNN and incorporated spatial asymmetry for graph coarsening. We conducted experiments using the publicly available datasets SEED and DEAP, separately for subject-dependent and subject-independent, to evaluate the performance of our model in emotion classification. Experimental results demonstrated that our method achieved state-of-the-art (SOTA) classification performance in both subject-dependent and subject-independent experiments. Furthermore, the visualization analysis of the learned graph structure reveals EEG channel connections that are significantly related to emotion and suppress irrelevant noise. These findings are consistent with established neuroscience research and demonstrate the potential of our approach in comprehending the neural underpinnings of emotion.

Spatial–Temporal Similarity Fusion Graph Adversarial Convolutional Networks for traffic flow forecasting

Traffic flow forecasting is integral to the advancement of intelligent transportation systems and the development of smart cities. This paper introduces a novel model, the Spatial–Temporal Similarity Fusion Graphs Adversarial Convolutional Networks (STSF-GACN), which leverages advanced data preprocessing techniques to enhance the predictive accuracy and efficiency of traffic flow forecasting.The innovation of our approach lies in the meticulous construction of the spatial–temporal similarity matrix through the precise calculation of temporal and spatial similarities. This matrix forms the backbone of our model, serving as the generator in the integrated Generative Adversarial Network (GAN) architecture. The Spatial–Temporal Similarity Fusion Adaptive Graph Convolutional Network, developed as part of our GAN’s generator, utilizes cutting-edge techniques such as the Wasserstein distance and Dynamic Time Warping to optimize the adaptive adjacency matrix, enabling the model to capture latent spatial–temporal correlations with unprecedented depth and precision.The discriminator of the GAN further refines the model by evaluating the accuracy of the traffic predictions, ensuring that the generative model produces results that are not only accurate but also robust against varying traffic conditions. This cohesive integration of GAN into the model architecture allows for a significant improvement in prediction accuracy and convergence speed, moving beyond traditional forecasting methods.

A novel structural deformation prediction method based on graph convolutional network during shield tunnel construction

During shield tunneling through existing steel reinforced concrete structures, superstructure deformation is an important parameter that reflects the disturbance degree of engineering construction to existing structure. Precisely predicting structural deformation can help engineers adjust shield machine operational parameters and ensure the success of the project. There has been no attempt to study the feasibility and applicability of machine learning for predicting structural deformation when shield machine cut through existing structure. To address this problem, this paper proposes a novel hybrid model (DSGCN-TCN), combining dynamic spatial graph convolutional network (DSGCN) and temporal convolutional network (TCN), to predict structural deformation. First, dynamic adjacency matrix is constructed based on correlation coefficient and attention mechanism to describe the dynamic change of irregular graph structure. Then dynamic adjacency matrices and feature matrices as the input of the GCN model to extract the dynamic spatial feature of structural deformation data. Followed by TCN and attention layer to capture the temporal correlation of structural deformation data. Finally, the prediction performance of the proposed method is verified using measured data from practical engineering. The experiment results show that compared with the selected baseline models and sub-models, the proposed model can predict the structural deformation more accurately.

Identification of Multi-Microgrid Clusters Using Terminal Spectral Clustering Algorithm

In response to the increasing impact of extreme weather on power distribution networks (PDNs), prioritizing resilience is imperative. This study introduces an innovative k-means spectral clustering algorithm to define the boundaries of microgrids (MGs) within a multi-microgrid (MMG) system. The aim is to improve reliability by clustering PDNs into resilient MGs. The power systems are modeled with nodes representing buses, and connections are represented as edges. The analysis involves computing the adjacency matrix, degree matrix, Laplacian matrix, and applying k-means clustering to group buses based on terminal point features. Silhouette coefficients (SC) are calculated to assess the quality of the clustering. The proposed method is tested on three IEEE distribution systems: IEEE 33, 69, and 118 bus systems. Findings reveal distinct clusters within each system with SC values above 0.68, particularly emphasizing the significance of terminal points as the basis for assisting power engineers in decision-making for predetermined grid partitioning.

Graph neural network incorporating time-varying frequency domain features with application in spatial wind speed field prediction

Precise forecasting of wind speed is vital to guarantee safe travel on bridges. Nevertheless, current research primarily concentrates on single-point prediction. When it comes to forecasting spatial wind fields, graph neural networks prove to be powerful methods, but many of them have yet to take into account the impact of frequency domain attributes. To address this, a novel model called the graph neural network with time-varying frequency features (GTF) is proposed. Its core layer employs wavelet transforms in matrix form to extract various frequency sub-series, followed by the use of adaptive adjacency matrices to identify their spatial characteristics. Furthermore, aggregating all frequency band information and exploring spatial features further through multi-kernel convolutions. The predictive performance of different models for wind speed forecasting is assessed by utilizing spatial wind field data collected on a large-span bridge. Experimental results demonstrate that spatiotemporal model GTF outperforms the other models in terms of predictive accuracy. The quantity of wind observation points and their level of correlation exert a certain impact on the GTF model, while hyperparameters such as stacking depth and wavelet decomposition parameters have minimal effects. Finally, recommended parameters for the GTF model are provided.

An Enhanced Credit Risk Evaluation by Incorporating Related Party Transaction in Blockchain Firms of China

Related party transactions (RPTs) can serve as channels for the spread of credit risk events among blockchain firms. However, current credit risk-assessment models typically only consider a firm’s individual characteristics, overlooking the impact of related parties in the blockchain. We suggest incorporating RPT network analysis to improve credit risk evaluation. Our approach begins by representing an RPT network using a weighted adjacency matrix. We then apply DANE, a deep network embedding algorithm, to generate condensed vector representations of the firms within the network. These representations are subsequently used as inputs for credit risk-evaluation models to predict the default distance. Following this, we employ SHAP (Shapley Additive Explanations) to analyze how the network information contributes to the prediction. Lastly, this study demonstrates the enhancing effect of using DANE-based integrated features in credit risk assessment.

HyGate-GCN: Hybrid-Gate-Based Graph Convolutional Networks with dynamical ratings estimation for personalized POI recommendation

The presence of user-generated ratings has dramatically facilitated the development of recommendation systems to aid users in discovering relevant and personalized points of interest (POI). It is worth mentioning that users’ choices and preferences are not static but rather dynamic, reflecting the ever-changing nature of human experiences and influences. Furthermore, the utilization of social influence and geographical proximity of users is still insufficient to capture the homophily effect within networks. In this paper, an interesting Hybrid Gate-based Graph Convolutional Network (HyGate-GCN) combining with feature vectors embedding and interaction, where a modified gated-GCN is proposed for personalized recommendations by adequately employing the behavior of users’ check-ins, temporal properties of users’ decisions, social properties of users, as well as the user/POI profile information data. Specifically, a novel POI graph reflecting the geographical proximity is first established to describe the behavior of users’ check-ins and, at the same time, an improved overlap ratio about POIs is employed to effectively describe temporal properties of users’ decisions. Then, an attention mechanism is developed to encode feature vectors of both the users and POIs, with the objective of assigning higher importance to features that are deemed relevant. Furthermore, a temporal Kalman filter dynamically estimating ratings is developed to exploit the information about the evolving preferences of users over time. Finally, a modified gated-GCN model with merging and refining gates is constructed to effectively acquire the homophily phenomenon in both trust network graphs and spatial adjacency matrix graphs of users and POIs respectively. Experimental results provide evidence of the effectiveness of our approach in improving accuracy and personalization.

A Study on Stock Price Prediction Based on Attention GCN-BiLSTM Modeling

It is of great significance to accurately predict stock price movements. By combining the R-Vine-Copula structure with the relationship between the conceptual sectors to which the stocks belong, the price correlation between stocks is measured and the adjacency matrix is constructed, and the model AGLSTM, which is constructed by combining the temporal attention mechanism, Graph Convolutional Neural Network and Bi-directional Long and Short-Term Memory Neural Network, is proposed to predict the price of 46 stocks from the constituent stocks of the SSE 50 by modeling them. The experimental results show that, compared with the baseline, the AGLSTM can predict the stock price. The experimental results show that compared with the baseline model, the MAE and RMSE results of the AGLSTM model predicted one step forward outperform all the comparison models, and the MAPE results are close to the best baseline model results. The results of MAPE are close to those of the best baseline model. Moreover, good results are also achieved in the experiment of multi-step forward prediction, which demonstrates the ability of AGLSTM model in long-term prediction and can provide some reference for investors to make investment decisions.

Fuzzy and Neutrosophic Cognitive Maps Analysis of the Emergence of COVID-19 Post-vaccination

After several years of the spread of coronavirus disease 2019 (COVID-19) around the world occurred, World Health Organization (WHO) has stimulated great efforts to develop a vaccine against the COVID-19. Therefore, all of citizen is obliged to take the vaccine for precaution. However, the vaccine is only one step to reduce the spreadness of COVID-19, where the appearance of COVID-19 can occur after vaccination. Some peoples do not understand the vaccine function where it is used to prevent spreading COVID-19. This research analysed the emergence of COVID-19 post-vaccination by using the method of fuzzy and neutrosophic cognitive maps. The collected data from an interview with two experts called as a concept and from there the directed graph and adjacency matrix are constructed. Multiplication between vectors and matrices are repeated until the fixed point in finding the hidden pattern for all the concepts for COVID-19 post-vaccination obtained. The results obtained from this study are useful to all to know the factors caused of the epidemic after vaccinated as well as the procedures to be followed to protect from this disease.

MDD brain network analysis based on EEG functional connectivity and graph theory

BackgroundExisting studies have shown that the brain network of major depression disorder (MDD) has abnormal topologies. However, constructing reliable MDD brain networks is still an open problem. New methodThis paper proposed a reliable MDD brain network construction method. First, seven connectivity methods are used to calculate the correlation between channels and obtain the functional connectivity matrix. Then, the matrix is binarized using four binarization methods to obtain the EEG brain network. Besides, we proposed an improved binarization method based on the criterion of maximizing differences between groups: the adaptive threshold (AT) method. The AT can automatically set the optimal binarization threshold and overcome the artificial influence of traditional methods. After that, several network metrics are extracted from the brain network to analyze inter-group differences. Finally, we used statistical analysis and Fscore values to compare the performance of different methods and establish the most reliable method for brain network construction. ResultsIn theta, alpha, and total frequency bands, the clustering coefficient, global efficiency, local efficiency, and degree of the MDD brain network decrease, and the path length of the MDD brain network increases. Comparison with existing methodsThe results show that AT outperforms the existing binarization methods. Compared with other methods, the brain network construction method based on phase-locked value (PLV) and AT has better reliability. ConclusionsMDD has brain dysfunction, particularly in the frontal and temporal lobes.

Fusion Network for Aspect-Level Sentiment Classification Based on Graph Neural Networks—Enhanced Syntactics and Semantics

Aspect-level sentiment classification (ALSC) struggles with correctly trapping the aspects and corresponding sentiment polarity of a statement. Recently, several works have combined the syntactic structure and semantic information of sentences for more efficient analysis. The combination of sentence knowledge with graph neural networks has also proven effective at ALSC. However, there are still limitations on how to effectively fuse syntactic structure and semantic information when dealing with complex sentence structures and informal expressions. To deal with these problems, we propose an ALSC fusion network that combines graph neural networks with a simultaneous consideration of syntactic structure and semantic information. Specifically, our model is composed of a syntactic attention module and a semantic enhancement module. First, the syntactic attention module builds a dependency parse tree with the aspect term being the root, so that the model focuses better on the words closely related to the aspect terms, and captures the syntactic structure through a graph attention network. In addition, the semantic enhancement module generates the adjacency matrix through self-attention, which is processed by the graph convolutional network to obtain the semantic details. Lastly, the extracted features are merged to achieve sentiment classification. As verified by experiments, the model we propose can effectively enhance ALSC’s behavior.

Alternating nonnegative least squares-incorporated regularized symmetric latent factor analysis for undirected weighted networks

An Undirected Weighted Network (UWN) can be precisely quantified as an adjacency matrix whose inherent characteristics are fully considered in a Symmetric Nonnegative Latent Factor (SNLF) model for its good representation accuracy. However, an SNLF model uses a sole latent factor matrix to precisely describe the topological characteristic of a UWN, i.e., symmetry, thereby impairing its representation learning ability. Aiming at addressing this issue, this paper proposes an Alternating nonnegative least squares-incorporated Regularized Symmetric Latent factor analysis (ARSL) model. First of all, equation constraints composed of multiple matrices are built in its learning objective for well describing the symmetry of a UWN. Note that it adopts an L2-norm-based regularization scheme to relax such constraints for making such a symmetry-aware learning objective solvable. Then, it designs an alternating nonnegative least squares-incorporated algorithm for optimizing its parameters efficiently. Empirical studies on four UWNs demonstrate that an ARSL model outperforms the state-of-the-art models in terms of representation accuracy, as well as achieves promising computational efficiency.

G-EEGCS: Graph-based optimum electroencephalogram channel selection

Electroencephalography (EEG) is commonly used to measure brain activity in clinical research. However, the abundance of channels in EEG data poses several challenges, including increased computational complexity, noise interference, and decreased efficiency in data analysis. A new graph-based method called G-EEGCS has been developed to address these issues for EEG channel selection. The graph-based optimum EEG channel selection (G-EEGCS) method constructs a directed network by establishing channel connections based on their pairwise correlations. Statistical features are used to determine similarity, and an adjacency matrix is created to represent the connectivity between the EEG channels. The influence of each channel on information flow within the network is assessed using the centrality measures. By calculating the shortest paths between all channel pairs, the algorithm quantifies the probability of each channel serving as a bridge between different parts of the graph. Channels with high centrality scores, indicating their significance in the information flow, are given priority during the selection process. An adaptive threshold is applied to optimize channel selection, ensuring that only channels that exceed the threshold, exhibit specific characteristics, and align with the overall network structure are retained. This adaptive thresholding mechanism enhances the robustness and flexibility of the G-EEGCS method, enabling personalized channel selection tailored to individual EEG datasets. The G-EEGCS approach offers a promising solution for EEG channel selection, improving the interpretability and efficiency of EEG-based studies and applications for researchers. It achieved an average accuracy of 0.9125, outperforming state-of-the-art methods. This method provides a valuable means of addressing the challenges posed by the multitude of channels in EEG data, ultimately contributing to more effective and insightful analysis in clinical research.

Homotopy properties of the complex of frames of a unitary space

AbstractLet be a finite‐dimensional vector space equipped with a nondegenerate Hermitian form over a field . Let be the graph with vertex set the one‐dimensional nondegenerate subspaces of and adjacency relation given by orthogonality. We give a complete description of when is connected in terms of the dimension of and the size of the ground field . Furthermore, we prove that if , then the clique complex of is simply connected. For finite fields , we also compute the eigenvalues of the adjacency matrix of . Then, by Garland's method, we conclude that for all , where is a field of characteristic 0, provided that . Under these assumptions, we deduce that the barycentric subdivision of deformation retracts to the order complex of the certain rank selection of that is Cohen–Macaulay over . Finally, we apply our results to the Quillen poset of elementary abelian ‐subgroups of a finite group and to the study of geometric properties of the poset of nondegenerate subspaces of and the poset of orthogonal decompositions of .

Medium–Long-Term PV Output Forecasting Based on the Graph Attention Network with Amplitude-Aware Permutation Entropy

Medium–long-term photovoltaic (PV) output forecasting is of great significance to power grid planning, power market transactions, power dispatching operations, equipment maintenance and overhaul. However, PV output fluctuates greatly due to weather changes. Furthermore, it is frequently challenging to ensure the accuracy of forecasts for medium–long-term forecasting involving a long time span. In response to the above problems, this paper proposes a medium–long-term forecasting method for PV output based on amplitude-aware permutation entropy component reconstruction and the graph attention network. Firstly, the PV output sequence data are decomposed by ensemble empirical mode decomposition (EEMD), and the decomposed intrinsic mode function (IMF) subsequences are combined and reconstructed according to the amplitude-aware permutation entropy. Secondly, the graph node feature sequence is constructed from the reconstructed subsequences, and the mutual information of the node feature sequence is calculated to obtain the graph node adjacency matrix which is applied to generate a graph sequence. Thirdly, the graph attention network is utilized to forecast the graph sequence and separate the PV output forecasting results. Finally, an actual measurement system is used to experimentally verify the proposed method, and the outcomes indicate that the proposed method, which has certain promotion value, can improve the accuracy of medium–long-term forecasting of PV output.

Hebbian spatial encoder with adaptive sparse connectivity

Biologically plausible neural networks have demonstrated efficiency in learning and recognizing patterns in data. This paper proposes a general online unsupervised algorithm for spatial data encoding using fast Hebbian learning. Inspired by the Hierarchical Temporal Memory (HTM) framework, we introduce the SpatialEncoder algorithm, which learns the spatial specialization of neurons’ receptive fields through Hebbian plasticity and k-WTA (k winners take all) inhibition. A key component of our model is a two-part synaptogenesis algorithm that enables the network to maintain a sparse connection matrix while adapting to non-stationary input data distributions. In the MNIST digit classification task, our model outperforms the HTM SpatialPooler in terms of classification accuracy and encoding stability. Compared to another baseline, a two-layer artificial neural network (ANN), our model achieves competitive classification accuracy with fewer iterations required for convergence. The proposed model offers a promising direction for future research on sparse neural networks with adaptive neural connectivity.

Sincronismo em um modelo metapopulacional de agregação com acoplamento não linear convexo

The present work is part of the result of the author's doctoral dissertation and aims at presenting a metapopulational aggregation model with a density-independent migration rate that allows the choice of the destination site according to its density. A non-linear coupling is produced here, formed by a convex combination of two matrices, one with a local connection and the other with a global connection. The result obtained here guarantees the asymptotic stability of the synchronized attractor and also that the transverse Lyapunov number of the synchronized attractor is given by the product of the orbital Lyapunov number by a quantifier that depends on the migration rate and the eigenvalues of an originating matrix of the connection matrix. From the numerical simulations of the variation of the transversal Lyapunov number in relation to the parameters migration rate and intrinsic reproduction rate of the function that describes the local dynamics, the regions of possible and impossible synchrony are measured. With the simulations of the synchronized orbit with respect to small perturbations, the values of the intrinsic reproduction rate and the migration rate are determined, for which the most synchronization occurs, and it is also determined that there is no synchronization of chaotic orbits.

Configuration synthesis and screening method for multiple closed-loop unit tandem mechanisms

To broaden the methods of configuration synthesis, this study proposes a new method for configuration synthesis and screening of multiple closed-loop unit tandem mechanisms. Firstly, some closed-loop configurations are taken as basic units, and the closed-loop basic units are synthesized in series under the condition of considering the basic unit types, contacts, and input and output relationships. Secondly, the connectivity of the mechanism is obtained by weighting the adjacency matrix, and the entropy weight method is used for the first time to establish a comprehensive evaluation index coefficient to assess the quality of the mechanism. Then, an improved simulated annealing-greedy algorithm is proposed and an algorithm software screening platform is built to screen mechanisms. Finally, the multi-fingered grasper is used as design case to verify the practicality of the proposed configuration synthesis and screening method. This study can provide a reference for theoretical research on the configuration synthesis and screening methods of multiple closed-loop unit tandem mechanisms.