Graph Matrix Research Articles

Integrated Extraction of Entities and Relations via Attentive Graph Convolutional Networks

For information security, entity and relation extraction can be applied in sensitive information protection, data leakage detection, and other aspects. The current approaches to entity relation extraction not only ignore the relevance and dependency between name entity recognition and relation extraction but also may result in the cumulative propagation of errors. To solve this problem, it is proposed that an end-to-end joint entity and relation extraction model based on the Attention mechanism and Graph Convolutional Network (GCN) to simultaneously extract named entities and their relationships. The model includes three parts: the detection of entity span, the construction of an entity relation weighted graph, and the inference of entity relation type. Firstly, the detection of entity spans is viewed as a sequence labeling problem, and a multi-feature fusion approach for word embedding representation is designed to calculate all entity spans in a sentence to form an entity span matrix. Secondly, the entity span matrix is employed in the Multi-Head Attention mechanism for constructing the weighted adjacency matrix of the entity relation graph. Finally, for the inference of entity relation type, considering the interaction between entities and relations, the entity span matrix and relation connection matrix are simultaneously fed into the GCN for integrated extraction of entities and relations. Our model is evaluated on the public NYT dataset, attaining a precision of 66.4%, a recall of 63.1%, and an F1 score of 64.7% for joint entity and relation extraction, significantly outperforming other approaches. Experiments demonstrate that the proposed model is helpful for inferring entities and relations, considering the interaction between entities and relations through the Attention mechanism and GCN.

Remaining useful life prediction with spatio-temporal graph transform and weakly supervised adversarial network: An application in power components

Remaining useful life (RUL) prediction is crucial in improving the reliability of insulated gate bipolar transistors (IGBTs) and has attracted widespread attention all over the world. Owing to the heterogeneity and complex internal connectivity of the IGBTs, accurate RUL prediction by traditional deep learning (DL) methods remains challenging. Herein, a novel prognostic framework is proposed for their RUL prediction. In brief, the non-smooth spike voltage of IGBTs is transformed into a graph matrix that contains rich correlation information. Then, spatio-temporal fusion graph network (STFGN) is proposed to realize RUL prediction. It contains spatial-scale and temporal-scale extractors, where the former one based on GraphSage can obtain unique IGBTs data structure information, while the latter based on bidirectional long short-term memory (BiLSTM) captures the time-series degradation features of IGBTs. Moreover, the weakly supervised adversarial learning strategy is considered to realize cross-domain prediction using scarce labeled data, which enhance the positive transfer. Four transfer tasks under variable working conditions are considered to prove the proposed method. The experimental results demonstrate that the average SF and RMSE metrics of the proposed method are 0.429 and 0.108, which is superior to other related methods.

Physics-informed line graph neural network for power flow calculation.

Power flow calculation plays a significant role in the operation and planning of modern power systems. Traditional numerical calculation methods have good interpretability but high time complexity. They are unable to cope with increasing amounts of data in power systems; therefore, many machine learning based methods have been proposed for more efficient power flow calculation. Despite the good performance of these methods in terms of computation speed, they often overlook the importance of transmission lines and do not fully consider the physical mechanisms in the power systems, thereby weakening the prediction accuracy of power flow. Given the importance of the transmission lines as well as to comprehensively consider their mutual influence, we shift our focus from bus adjacency relationships to transmission line adjacency relationships and propose a physics-informed line graph neural network framework. This framework propagates information between buses and transmission lines by introducing the concepts of the incidence matrix and the line graph matrix. Based on the mechanics of the power flow equations, we further design a loss function by integrating physical information to ensure that the output results of the model satisfy the laws of physics and have better interpretability. Experimental results on different power grid datasets and different scenarios demonstrate the accuracy of our proposed model.

A Laplacian eigenbasis for threshold graphs

Abstract Let G G be a graph on n n vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order n n is also an eigenbasis of G G if and only if G G is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs that are weakly Hadamard diagonalizable.

On the eigenvalues of the distance signless Laplacian matrix of graphs

Let G be a connected graph and let DQ(G) be the distance signless Laplacian matrix of G with eigenvalues ρ1≥ ρ2≥…≥ ρn. The spread of the matrix DQ}(G) is defined as s(DQ(G)) := maxi,j| ρi-ρj| = ρ1- ρn. We derive new bounds for the distance signless Laplacian spectral radius ρ1 of G. We establish a relationship between the distance signless Laplacian energy and the spread of DQ(G). For a real number α ≠ 0, the graph invariant mα (G) is the sum of the α -th power of the distance signless Laplacian eigenvalues of G. Finally, we obtain various bounds for the graph invariant mα(G).

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions.

Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization

In traditional adaptive neighbors graph learning (ANGL)-based clustering, the time complexity is more than O(n2), where n is the number of data points, which is not scalable for large-scale data problems in real applications. Subsequently, ANGL adds a balance regularization to its objective function to avoid the sparse over-fitting problem in the learned similarity graph matrix. Still, the regularization may leads to many weak connections between data points in different clusters. To address these problems, we propose a new fast clustering method, namely, Adaptive Neighbors Graph Learning for Large-Scale Data Clustering using Vector Quantization and Self-Regularization (ANGL-LDC), to perform vector quantization (VQ) on original data and feed the obtained VQ data as the input in the n×n similarity graph matrix learning. Hence, the n×n similarity graph matrix learning problem is simplified to weighted m×m(m≪n) graph learning problem, where m is the number of distinct points and weight is the duplicate times of distinct points in VQ data. Consequently, the time complexity of ANGL-LDC is much lower than that of ANGL. At the same time, we propose a new ANGL objective function with a graph connection self-regularization mechanism, where the ANGL-LDC objective function will get an infinity value if the value of one graph connection is equal to 1. Therefore, ANGL-LDC naturally avoids obtaining the sparse over-fitting problem since we need to minimize the value of ANGL-LDC’s objective function. Experimental results on synthetic and real-world datasets demonstrate the scalability and effectiveness of ANGL-LDC.

Structural graph learning method for hyperspectral band selection

ABSTRACT Recently, graph learning-based hyperspectral band selection algorithms illustrate impressive performance for hyperspectral image (HSI) processing, whose goal is to select an optimal band combination containing less redundancy through the learned graph matrix. However, most of the previous methods work in single spectral domain, which neglects the rich image spatial information. Moreover, they typically model the graph matrix from a global perspective while ignoring the differences in spatial distribution that exist in diverse pixel and band regions. Based on the above considerations, to take full account of structure information in spatial and spectral domains, a structural graph learning method for hyperspectral band selection (SGLM) is designed. Specifically, SGLM constructs two matrices using the correlation between pixels and bands under the local perspective, which can capture the image structure information reasonably. Since the proposed method is modelled in both spatial and spectral dimensions, it is conducive to subsequent band subset generation task. Meanwhile, in order to guarantee local spatial consistency among bands, a Laplacian regularization term associated with the error matrix is introduced to the self-representation model. Additionally, considering that the importance of a band is consistent with its capability to reconstruct the entire band set, an adjacent bands reconstruction strategy is adopted to obtain the ultimate band combination, which can assess the significance of each band effectively. The comprehensive experimental analysis on four datasets demonstrates that the proposed SGLM model has outstanding superiority in comparison with several band selection algorithms.

G[formula omitted]BFNN: Generalized geodesic basis function neural network

Real-world data is typically distributed on low-dimensional manifolds embedded in high-dimensional Euclidean spaces. Accurately extracting spatial distribution features on general manifolds that reflect the intrinsic characteristics of data is crucial for effective feature representation. Therefore, we propose a generalized geodesic basis function neural network (G2BFNN) architecture. The generalized geodesic basis functions (G2BF) are defined based on generalized geodesic distances. The generalized geodesic distance metric (G2DM) is obtained by learning the manifold structure. To implement this architecture, a specific G2BFNN, named discriminative local preserving projection-based G2BFNN (DLPP-G2BFNN) is proposed. DLPP-G2BFNN mainly contains two modules, namely the manifold structure learning module (MSLM) and the network mapping module (NMM). In the MSLM module, a supervised adjacency graph matrix is constructed to constrain the learning of the manifold structure. This enables the learned features in the embedding subspace to maintain the manifold structure while enhancing the discriminability. The features and G2DM learned in the MSLM are fed into the NMM. Through the G2BF in the NMM, the spatial distribution features on manifold are obtained. Finally, the output of the network is obtained through the fully connected layer. Compared with the local response neural network based on Euclidean distance, the proposed network can reveal more essential spatial structure characteristics of the data. Meanwhile, the proposed G2BFNN is a generalized network architecture that can be combined with any manifold learning method, showcasing high scalability. The experimental results demonstrate that the proposed DLPP-G2BFNN outperforms existing methods by utilizing fewer kernels while achieving higher recognition performance.

Spectral Properties of Dual Unit Gain Graphs

In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers have found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if, and only if, the dual gain graph is balanced. By using dual cosine functions, we establish the closed form of the eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too.

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.

Clique-like Point Cloud Registration: A Flexible Sampling Registration Method Based on Clique-like for Low-Overlapping Point Cloud.

Three-dimensional point cloud registration is a critical task in 3D perception for sensors that aims to determine the optimal alignment between two point clouds by finding the best transformation. Existing methods like RANSAC and its variants often face challenges, such as sensitivity to low overlap rates, high computational costs, and susceptibility to outliers, leading to inaccurate results, especially in complex or noisy environments. In this paper, we introduce a novel 3D registration method, CL-PCR, inspired by the concept of maximal cliques and built upon the SC2-PCR framework. Our approach allows for the flexible use of smaller sampling subsets to extract more local consensus information, thereby generating accurate pose hypotheses even in scenarios with low overlap between point clouds. This method enhances robustness against low overlap and reduces the influence of outliers, addressing the limitations of traditional techniques. First, we construct a graph matrix to represent the compatibility relationships among the initial correspondences. Next, we build clique-likes subsets of various sizes within the graph matrix, each representing a consensus set. Then, we compute the transformation hypotheses for the subsets using the SVD algorithm and select the best hypothesis for registration based on evaluation metrics. Extensive experiments demonstrate the effectiveness of CL-PCR. In comparison experiments on the 3DMatch/3DLoMatch datasets using both FPFH and FCGF descriptors, our Fast-CL-PCRv1 outperforms state-of-the-art algorithms, achieving superior registration performance. Additionally, we validate the practicality and robustness of our method with real-world data.

Inverse of the squared distance matrix of a complete multipartite graph

Let $G$ be a connected graph on $n$ vertices and $d_{ij}$ be the length of the shortest path between vertices $i$ and $j$ in $G$. We set $d_{ii}=0$ for every vertex $i$ in $G$. The squared distance matrix $\Delta(G)$ of $G$ is the $n\times n$ matrix with $(i,j)^{th}$ entry equal to $0$ if $i = j$ and equal to $d_{ij}^2$ if $i \neq j$. For a given complete $t$-partite graph $K_{n_1,n_2,\cdots,n_t}$ on $n=\sum_{i=1}^t n_i$ vertices, under some condition we find the inverse $\Delta(K_{n_1,n_2,\cdots,n_t})^{-1}$ as a rank-one perturbation of a symmetric Laplacian-like matrix $\mathcal{L}$ with $\text{rank} (\mathcal{L})=n-1$. We also investigate the inertia of $\mathcal{L}$.

Combining improved DFMEA with knowledge graph for component risk analysis of complex products

With the development of information technology in manufacturing, product lifecycle iteration is accelerating. Efficiently analyzing and identifying component risks is important to ensure the reliability of products. This paper proposes a new method that combines improved design failure mode and effect analysis (DFMEA) with the knowledge graph for component risk analysis of complex products. A risk evaluation knowledge graph is built for the risk identification and knowledge provision in the process of DFMEA. Graph analysis is used to identify to-be-evaluated objectives based on historical maintenance data, which helps designers avoid the heavy task of identification. The graph matrix of the historical evaluations is used to calculate the comprehensive weights. A Dempster-Shafer (DS) evidence fusion method based on comprehensive weight evaluation information is proposed for the effective fusion of evaluation evidence. As an alternative to the exact risk ranking, we offer a risk trade-off VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) method for components classification that classifies components into different risk classes for different risk treatment measures. Finally, the proposed method is validated using a tunnel boring machine as an example, and comparison and sensitivity analyses are performed to demonstrate that the risk value shows a consistent and stable change with expert evaluation.

Spectral properties of Sombor matrix of threshold graphs

We investigate the Sombor spectral properties of threshold graphs, a formula for the Sombor index is presented, the Sombor eigenvalues are given, graphs with simple Sombor eigenvalues are characterized, bounds on the smallest/largest Sombor eigenvalues are presented, the multiplicities of the Sombor eigenvalues are discussed, formulae for trace and determinant of the associated quotient matrix are given, the Sombor spread bound and the bounds on the Sombor energy along with the characterization of extremal graphs. At the end, the conclusion states that all our results are valid for adjacency matrix and other adjacency type matrices.

Brain Connectivity Dynamics and Mittag–Leffler Synchronization in Asymmetric Complex Networks for a Class of Coupled Nonlinear Fractional-Order Memristive Neural Network System with Coupling Boundary Conditions

This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, or Parkinson’s disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients.

Energy and spectral radius of Zagreb matrix of graph with applications

Energy and spectral radius of Zagreb matrix of graph with applications

Statistical physics of principal minors: Cavity approach.

Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem is to compute the sum of powers of principal minors of a matrix which is relevant to the study of critical behaviors in quantum fermionic systems and finding a subset of maximally informative training data for a learning algorithm. Specifically, principal minors of positive square matrices can be considered as statistical weights of a random point process on the set of the matrix indices. The probability of each subset of the indices is in general proportional to a positive power of the determinant of the associated submatrix. We use Gaussian representation of the determinants for symmetric and positive matrices to estimate the partition function (or free energy) and the entropy of principal minors within the Bethe approximation. The results are expected to be asymptotically exact for diagonally dominant matrices with locally treelike structures. We consider the Laplacian matrix of random regular graphs of degree K=2,3,4 and exactly characterize the structure of the relevant minors in a mean-field model of such matrices. No (finite-temperature) phase transition is observed in this class of diagonally dominant matrices by increasing the positive power of the principal minors, which here plays the role of an inverse temperature.

The Smith normal form of the walk matrix of the Dynkin graph An

In this paper, we give the rank of the walk matrix of the Dynkin graph An, and prove that its Smith normal form isdiag(1,…,1︸⌈n2⌉,0,…,0).

Fault identification of centrifugal pump using WGAN-GP method with unbalanced datasets based on kinematics simulation and experimental case

Abstract In practical engineering applications, the accuracy and stability of fault identification for centrifugal pump will be significantly reduced due to unbalanced distribution between normal and fault datasets, i.e., the number of normal working samples is far more than the fault samples. To alleviate this bottleneck issue, this paper explores the fault identification of centrifugal pump based on Wasserstein generative adversarial network with gradient penalty (WGAN-GP) through combining kinematics simulation and experimental case. Specifically, ideal unbalanced vibration datasets from failure patterns such as damaged impeller of centrifugal pump are simulated and collected by prototype ADAMS software, then the unbalanced vibration signals are transformed into 2D grey-scale images. Furtherly, the generated grey-scale image datasets are feed into the original grey-scale image dataset as new datasets for training when the Nash equilibrium of the WGAN-GP model is reached. Eventually, the fault patterns of centrifugal pump are identified using confusion matrix graph. Meanwhile, another public dataset of centrifugal pump is employed for verifying the accuracy of the WGAN-GP model. Results indicate that fault identification accuracies with 95.07% and 98.0% of both kinematics simulation and experimental case are obtained, respectively, and the issues of unbalanced distribution and insufficient dataset can be overcome effectively.