Adjacency Matrix Research Articles

Hypercomplex Graph Neural Network: Towards Deep Intersection of Multi-modal Brain Networks.

The multi-modal neuroimage study has provided insights into understanding the heteromodal relationships between brain network organization and behavioral phenotypes. Integrating data from various modalities facilitates the characterization of the interplay among anatomical, functional, and physiological brain alterations or developments. Graph Neural Networks (GNNs) have recently become popular in analyzing and fusing multi-modal, graph-structured brain networks. However, effectively learning complementary representations from other modalities remains a significant challenge due to the sophisticated and heterogeneous inter-modal dependencies. Furthermore, most existing studies often focus on specific modalities (e.g., only fMRI and DTI), which limits their scalability to other types of brain networks. To overcome these limitations, we propose a HyperComplex Graph Neural Network (HC-GNN) that models multi-modal networks as hypercomplex tensor graphs. In our approach, HC-GNN is conceptualized as a dynamic spatial graph, where the attentively learned inter-modal associations are represented as the adjacency matrix. HC-GNN leverages hypercomplex operations for inter-modal intersections through cross-embedding and cross-aggregation, enriching the deep coupling of multi-modal representations. We conduct a statistical analysis on the saliency maps to associate disease biomarkers. Extensive experiments on three datasets demonstrate the superior classification performance of our method and its strong scalability to various types of modalities. Our work presents a powerful paradigm for the study of multi-modal brain networks.

An Adaptive Framework for Traffic Congestion Prediction using Deep Learning

Aim and background: Congestion on China's roads has worsened in recent years due to the country's rapid economic development, rising urban population, rising private car ownership, inequitable traffic flow distribution, and growing local congestion. As cities expand, traffic congestion has become an unavoidable nuisance that endangers the safety and progress of its residents. Improving the utilization rate of municipal transportation facilities and relieving traffic congestion depend on a thorough and accurate identification of the current state of road traffic and necessitate anticipating road congestion in the city. Methodology: In this research, we suggest using a deep spatial and temporal graph convolutional network (DSGCN) to forecast the current state of traffic congestion. To begin, we grid out the transportation system to create individual regions for analysis. In this work, we abstract the grid region centers as nodes, and we use an adjacency matrix to signify the dynamic correlations between the nodes. Results and Discussion: The spatial correlation between regions is then captured utilizing a Graph Convolutional-Neural-Network (GCNN), while the temporal correlation is captured using a two-layer long and short-term feature model (DSTM). Conclusion: Finally, testing on real PeMS datasets shows that the DSGCN has superior performance than other baseline models and provides more accurate traffic congestion prediction.

DHKFN

Knowledge tracing is effective in modeling learners' knowledge levels to predict future answering situations based on their past learning history and interaction processes. However, current methods often overlook the impact of knowledge point correlations on answer prediction. This paper design a model based on deep hierarchical knowledge fusion networks (DHKFN). It utilizes statistical approaches to construct correlation matrices to capture the correlations between knowledge points. Subsequently, it constructs a topology graph structure of questions and knowledge points and utilizes a multi-head attention network to learn student interaction information from multiple perspectives, effectively constructing adjacency matrices. Finally, it uses GCN to learn the interaction information representation between deep-level knowledge points from dynamically constructed a topology graph structures. Experimental results on three large public datasets show that DHKFN effectively considers the influence of correlations between different knowledge points, thus showing promising effectiveness.

Pre-connected and trainable adjacency matrix-based GCN and neighbor feature approximation for industrial fault diagnosis

Industrial fault diagnosis methods based on graph convolution network (GCN) becomes a hot topic for its great feature extraction ability to multivariate time-series data. However, GCNs ignore inter-sample temporality when constructing the adjacency matrix (AM), leading to low prediction accuracy. A novel fault diagnosis method based on pre-connected and trainable AM-based GCN and neighbor feature approximation (PTGCN-FA) is proposed at the node-level task. Firstly, PTGCN-FA introduces the temporal nearest neighbors into spatial nearest neighbors to pre-connect and construct the AM. Then, the AM is trained only where the samples are connected, which makes the best weights obtained and reduces the time complexity of the model. Finally, after the GCN layers, the trained AM is introduced into the approximation of features, which are neighbors in the original sample space. Two process industry cases are carried out, and the simulation results including diagnosis accuracy, confusion matrix, study to the ratio of labeled data and an ablation experiment verify PTGCN-FA has more efficient and accurate diagnostic performance than related methods. Additionally, the analysis of the temporal neighborhood weight parameter shows that the performance of fault diagnosis can be improved by considering both temporal and spatial information between samples.

MSA-GCN: Multistage Spatio-Temporal Aggregation Graph Convolutional Networks for Traffic Flow Prediction

Timely and accurate traffic flow prediction is crucial for stabilizing road conditions, reducing environmental pollution, and mitigating economic losses. While current graph convolution methods have achieved certain results, they do not fully leverage the true advantages of graph convolution. There is still room for improvement in simultaneously addressing multi-graph convolution, optimizing graphs, and simulating road conditions. Based on this, this paper proposes MSA-GCN: Multistage Spatio-Temporal Aggregation Graph Convolutional Networks for Traffic Flow Prediction. This method overcomes the aforementioned issues by dividing the process into different stages and achieves promising prediction results. In the first stage, we construct a latent similarity adjacency matrix and address the randomness interference features in similarity features through two optimizations using the proposed ConvGRU Attention Layer (CGAL module) and the Causal Similarity Capture Module (CSC module), which includes Granger causality tests. In the second stage, we mine the potential correlation between roads using the Correlation Completion Module (CC module) to create a global correlation adjacency matrix as a complement for potential correlations. In the third stage, we utilize the proposed Auto-LRU autoencoder to pre-train various weather features, encoding them into the model’s prediction process to enhance its ability to simulate the real world and improve interpretability. Finally, in the fourth stage, we fuse these features and use a Bidirectional Gated Recurrent Unit (BiGRU) to model time dependencies, outputting the prediction results through a linear layer. Our model demonstrates a performance improvement of 29.33%, 27.03%, and 23.07% on three real-world datasets (PEMSD8, LOSLOOP, and SZAREA) compared to advanced baseline methods, and various ablation experiments validate the effectiveness of each stage and module.

The Singularity of Three Kinds of New Tricyclic Graphs

A graph G is singular if its adjacency matrix is singular. The starting vertices of two paths Pb1 and Pb2 are simultaneously bound to the ending vertex of the path Ps1, and the ending vertices of the paths Pb1 and Pb2 are bound to the starting vertex of path Ps2. Meanwhile, the starting vertex of the path Ps1 is bound to a vertex of the cycle Ca1, and the ending vertex of the path Ps2 is bound to a vertex of the cycle Ca2. Thus, the resulting graph is written as ξ(a1,a2,b1,b2,s1,s2). This is denoted by ζ(a1,a2,b1,b2,s)=ξ(a1,a2,b1,b2,1,s) and ε(a1,a2,b1,b2)=ζ(a1,a2,b1,b2,1), which are referred to as the ξ-graph, ζ-graph and ε-graph for short, respectively. It is known that there are 15 kinds of tricyclic graphs. The purpose of this paper is to study the necessary and sufficient conditions for ξ-graphs, ζ-graphs and ε-graphs to be singular graphs. We analyzed the structure of the elementary spanning subgraphs of the graph G=ξ(a1,a2,b1,b2,s1,s2). By calculating the determinant of the adjacency matrix of the graph G, the necessary and sufficient conditions for the determinant of the graph G to be zero is obtained, and so the necessary and sufficient conditions for graph ξ(a1,a2,b1,b2,s1,s2) to be singular are obtained. As the corollaries, the necessary and sufficient conditions for graphs ζ(a1,a2,b1,b2,s) and ε(a1,a2,b1,b2) to be singular are also obtained.

The Algebraic Entropies of the Leavitt Path Algebra and the Graph Algebra Agree

In this note we prove that the algebras LK(E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_K(E)$$\\end{document} and KE have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The main argument leans on (1) the holomorphic functional calculus; (2) the relation of entropy with suitable norm of the adjacency matrix; and (3) the Cohn path algebras which yield suitable bounds for the algebraic entropies.

MGHCN: Multi-graph structures and hypergraph convolutional networks for traffic flow prediction

Accurate and timely traffic flow predictions are essential for effective traffic management and congestion reduction. However, most traditional prediction methods often fail to capture the complex dynamics and correlations within traffic flows due to insufficient processing of spatiotemporal data. Specifically, these methods struggle to integrate and analyze the multi-layered spatial and temporal interactions inherent in traffic data, leading to suboptimal prediction accuracy and robustness. To address this limitation, this paper presents a Multi-Graph Structures and Hypergraph Convolutional Network (MGHCN) that combines diverse graphs and hypergraphs. The MGHCN simplifies the predictive framework by integrating key components that improve its robustness and accuracy. One of the most critical components is the dual hypergraph structure, which captures edge correlations by converting traditional graph edges into hypergraph nodes. To better capture the spatiotemporal correlation of traffic data, a Graph Convolutional Network (GCN) is employed to analyze these hypergraphs in depth. Finally, a novel adjacency matrix and a dynamic graph module are used to accurately simulate interactions between spatiotemporal features, thereby enhancing the accuracy and robustness of predictions. Experimental validation on four distinct real-world traffic datasets shows that MGHCN outperforms existing state-of-the-art traffic prediction methods.

Indoor Scene Intelligent Identification System Based on Spatial Topological Relationship Constraints

Abstract. Indoor scene identification can provide prior environmental information for indoor positioning applications, achieving positioning enhancement. Due to the similarity of wireless signals in adjacent spaces, it can lead to incorrect identification in neighbouring scenario units. To address this problem, this paper first employs a Naive Bayes classifier to train and classify wireless signal strength data from different scenes, constructing a scene identification algorithm. Secondly, a topological relationship adjacency matrix and adjacency list tailored for indoor positioning are constructed, imposing spatial topological constraints to assist scene identification. Finally, an indoor scene intelligent identification system is developed and implemented. The experimental results indicate that the scene identification method based on spatial topological relationship constraints can effectively improve identification accuracy. The overall accuracy for 8 scenario units is 98.2%, and the identification accuracy is increased by 1.1% compared with the original method.

Distinguishing between topological isomorphism and topological equivalence of power electronic converters

In the process of deducing the topology of power electronic converters, scholars often use topological equivalence or topological isomorphism to identify topologies with different structures but the same performance to avoid repeated research. However, the connotations of topological equivalence and topological isomorphism are not the same. This paper will clarify the method for accurately identifying topologies with the same performance by distinguishing the differences and connections between the two. First, it is derived that the necessary condition for topological isomorphism is that the determinants of their adjacency matrices are equal; then, it is derived that the necessary and sufficient conditions for topological equivalence are that their component composition is the same and their simple circuits correspond one to one; finally, the above two conditions are analyzed from the perspective of topological subgraphs, and it is found that topological isomorphism is a sufficient but not necessary condition for topological equivalence, and topological equivalence is a necessary and sufficient condition for the same topological performance. Therefore, in practice, equivalence rather than isomorphism should be used to identify topologies with the same performance. This paper verifies the correctness of the theoretical analysis through a case analysis. In addition, this paper also introduces a method for automatically determining equivalent topologies based on the depth-first search algorithm to help quickly and accurately identify converter topologies with the same performance.

Research on Smart City Road Network Capacity Optimization Configuration Based on Deep Learning Algorithms

At present, the urban traffic system is faced with the problems of congestion and low efficiency, and the traditional methods have certain limitations when dealing with the complex urban road network. This paper aims to explore a new method of capacity Optimization of Road Networks in a Smart City environment and proposes a method based on a Graph Neural network, named “Smart City Road optimization Graph Neural Network” (SCRO-GNN). SCRO-GNN first collects and preprocesses multi-source data, including road network data, traffic flow, accident records, environmental factors, etc. The key node and edge features, including the number of lanes at the intersection, the traffic flow of the section, and the adjacency matrix of the road network are defined to characterize the structure of the road network. Then, the graph neural network model is constructed and trained to predict the traffic flow of different sections and evaluate the road capacity by using the graph structure of the road network. This paper tests the performance of SCRO-GNN on real road networks in multiple cities. The results show that, compared with the traditional traffic flow prediction model, SCRO-GNN can significantly improve the prediction accuracy, especially when dealing with the highly complex urban road network structure. Based on these predictions, the proposed optimization strategy performed well in reducing traffic congestion and improving the efficiency of road use. The research in this paper not only demonstrates the potential of graph neural networks in smart city road network optimization, but also provides a new direction for future traffic system research. The successful implementation of the SCRO-GNN approach is expected to provide more efficient and intelligent solutions for urban traffic management and planning.

TG-PGAT: An AIS Data-Driven Dynamic Spatiotemporal Prediction Model for Ship Traffic Flow in the Port

Accurate prediction of ship traffic flow is essential for developing intelligent maritime transportation systems. To address the complexity of ship traffic flow data in the port and the challenges of capturing its dynamic spatiotemporal dependencies, a dynamic spatiotemporal model called Temporal convolutional network-bidirectional Gated recurrent unit-Pearson correlation coefficient-Graph Attention Network (TG-PGAT) is proposed for predicting traffic flow in port waters. This model extracts spatial features of traffic flow by combining the adjacency matrix and spatial dynamic coefficient correlation matrix within the Graph Attention Network (GAT) and captures temporal features through the concatenation of the Temporal Convolutional Network (TCN) and Bidirectional Gated Recurrent Unit (BiGRU). The proposed TG-PGAT model demonstrates higher prediction accuracy and stability than other classic traffic flow prediction methods. The experimental results from multiple angles, such as ablation experiments and robustness tests, further validate the critical role and strong noise resistance of different modules in the TG-PGAT model. The experimental results of visualization demonstrate that this model not only exhibits significant predictive advantages in densely trafficked areas of the port but also outperforms other models in surrounding areas with sparse traffic flow data.

Spectral Pseudorandomness and the Road to Improved Clique Number Bounds for Paley Graphs

We study subgraphs of Paley graphs of prime order p induced on the sets of vertices extending a given independent set of size a to a larger independent set. Using a sufficient condition due to Kunisky (2023), we show that estimates on a new family of necklace character sums would imply that, as p → ∞ , the empirical spectral distributions of the adjacency matrices of any sequence of such subgraphs have the same weak limit (after rescaling) as those of subgraphs induced on a random set including each vertex independently with probability 2 − a , namely, a Kesten-McKay law with parameter 2 a . We prove the necessary estimates for a = 1, obtaining in the process an alternate proof of a character sum equidistribution result of Xi (2022), and provide numerical evidence for this weak convergence for a ≥ 2 . We also conjecture that the minimum eigenvalue of any such sequence converges (after rescaling) to the left edge of the corresponding Kesten-McKay law, and provide numerical evidence for this convergence. Finally, we show that, once a ≥ 3 , this (conjectural) convergence of the minimum eigenvalue would imply bounds on the clique number of the Paley graph improving on the current state of the art due to Hanson and Petridis (2021), and that this convergence for all a ≥ 1 would imply that the clique number is o ( p ) .

Automatic Abelian Complexities of Parikh-Collinear Fixed Points

AbstractParikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT–WORDS 2023 we showed that fixed points of Parikh-collinear morphisms are automatic. We also showed that the abelian complexity function of a binary fixed point of such a morphism is automatic under some assumptions. In this note, we fully generalize the latter result. Namely, we show that the abelian complexity function of a fixed point of an arbitrary, possibly erasing, Parikh-collinear morphism is automatic. Furthermore, a deterministic finite automaton with output generating this abelian complexity function is provided by an effective procedure. To that end, we discuss the constant of recognizability of a morphism and the related cutting set.

From Noise to Knowledge: Diffusion Probabilistic Model-Based Neural Inference of Gene Regulatory Networks.

Understanding gene regulatory networks (GRNs) is crucial for elucidating cellular mechanisms and advancing therapeutic interventions. Original methods for GRN inference from bulk expression data often struggled with the high dimensionality and inherent noise in the data. Here we introduce RegDiffusion, a new class of Denoising Diffusion Probabilistic Models focusing on the regulatory effects among feature variables. RegDiffusion introduces Gaussian noise to the input data following a diffusion schedule and uses a neural network with a parameterized adjacency matrix to predict the added noise. We show that using this process, GRNs can be learned effectively with a surprisingly simple model architecture. In our benchmark experiments, RegDiffusion shows superior performance compared to several baseline methods in multiple datasets. We also demonstrate that RegDiffusion can infer biologically meaningful regulatory networks from real-world single-cell data sets with over 15,000 genes in under 5 minutes. This work not only introduces a fresh perspective on GRN inference but also highlights the promising capacity of diffusion-based models in the area of single-cell analysis. The RegDiffusion software package and experiment data are available at https://github.com/TuftsBCB/RegDiffusion.

Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model

Abstract We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma \in (0.5,1)$ depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017) Ann. Stat.45(1) 289–315.) for non-uniform HSBMs. Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest.

Predicting functional connectivity network from routinely acquired T1-weighted imaging-based brain network by generative U-GCNet

Predicting the function magnetic resonance imaging (fMRI)-based brain network (fMRI-BN) from structure MRI-based brain network is imperative in clinical practice because fMRIs are not routinely acquired in a vast majority of hospitals. In this study, a generative U-GCNet (U-shaped graph convolutional Network) was proposed to predict fMRI-BN from radiomics-based morphological brain network (radMBN) derived from routinely acquired T1-WI image. Specifically, the U-GCNet consisted of a graph convolutional network (GCN) encoder module (En-GCN), a deep feature connectivity construction module (DF2C), and a GCN decoder module (De-GCN). Both En-GCN and De-GCN employed mixed local-and-long distance node feature aggregation strategy to enhance the graph encoding and decoding ability, and the DF2C reshaped the deep feature matrix into the connectivity matrix for outputting the brain network prediction. Additionally, a multi-scale network similarity loss function was conducted on full values, upper triangular values, and each row values of connectivity matrix. Experiments on 3169 subjects from three publicly available databases demonstrated that the U-GCNet could predict the fMRI-BN from radMBN with a promising performance (MSE [0.0002 0.0025], PCC [0.956 0.991]) over eight alternative methods under comparison. The results exhibited a significant correlation (PCC [0.796, 0.897], P<0.05) between the estimated and real radiomics-function coupling values. The individual-level and group-level brain network visualization was displayed with high consistency. The TOP brain regions identified by four graph-based metrics also exhibited with consistency. These results demonstrated that the proposed U-GCNet could achieve promising prediction of fMRI-BN from radMBN which could alleviate the limited availability of fMRI and boost its usage in clinical practice.

Action recognition algorithm based on skeleton graph with multiple features and improved adjacency matrix

Action recognition algorithm based on skeleton graph with multiple features and improved adjacency matrix

Multimodal adversarial informer for highway vehicle lane-changing trajectory prediction

To enhance the perception of vehicle trajectory information and lane-changing decision-making capabilities in intelligent connected vehicles during multivehicle interaction scenarios, we propose a novel method based on a Multimodal Adversarial Informer (MAI) for highway multivehicle lane-changingrajectory prediction. This method achieves spatiotemporal features of target and surrounding vehicles through graph learning of temporal features and spatial adjacency matrices. Considering the heading angle and vehicle local X-axis displacement, the vehicle trajectory samples are categorized for training and validation of the multimodal Informer. A multi-criterion discriminator is utilized to judge whether the generated trajectory fits the requirements of accuracy and rationality. After adversarial learning, the optimal vehicle lane-changing trajectory prediction is obtained using the proposed MAI. Experiments conducted with the NGSIM dataset demonstrate the comparative performance of baseline models on three different noise-added testing datasets using MAE, RMSE, and R² metrics. The MAI model consistently outperforms the others, achieving the lowest MAE and RMSE and the highest R² values across all datasets, indicating superior predictive accuracy and fit. Furthermore, the results show that the proposed MAI framework maintains a relatively low prediction error over both short-term and long-term horizons compared to baseline models.

Spatially Informed Graph Structure Learning Extracts Insights from Spatial Transcriptomics.

Embeddings derived from cell graphs hold significant potential for exploring spatial transcriptomics (ST) datasets. Nevertheless, existing methodologies rely on a graph structure defined by spatial proximity, which inadequately represents the diversity inherent in cell-cell interactions (CCIs). This study introduces STAGUE, an innovative framework that concurrently learns a cell graph structure and a low-dimensional embedding from ST data. STAGUE employs graph structure learning to parameterize and refine a cell graph adjacency matrix, enabling the generation of learnable graph views for effective contrastive learning. The derived embeddings and cell graph improve spatial clustering accuracy and facilitate the discovery of novel CCIs. Experimental benchmarks across 86 real and simulated ST datasets show that STAGUE outperforms 15 comparison methods in clustering performance. Additionally, STAGUE delineates the heterogeneity in human breast cancer tissues, revealing the activation of epithelial-to-mesenchymal transition and PI3K/AKT signaling in specific sub-regions. Furthermore, STAGUE identifies CCIs with greater alignment to established biological knowledge than those ascertained by existing graph autoencoder-based methods. STAGUE also reveals the regulatory genes that participate in these CCIs, including those enriched in neuropeptide signaling and receptor tyrosine kinase signaling pathways, thereby providing insights into the underlying biologicalprocesses.