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This paper is concerned with a conflict that N -pursuers versus M -evaders. It is a multi-pursuer multi-evader game extended from classical differential game theory to simultaneously address target selection and multi-player pursuit-evasion. Every pursuer attempts to intercept the evader it has chosen as its target while every evader does the opposite. This is modeled as a multi-player nonzero-sum differential game under a weighted directed graph. Moreover, a novel and more practical framework, the Unique-Choice (UC) games framework, is provided. Hamilton–Jacobi–Isaacs (HJI) is used for solving the game to derive the optimal distributed control strategy for each player based on graph theory. An important but has not been extensively studied issue, target selection, is studied. Different from the former research, this paper proposes a more reasonable criterion for target selection which makes the cost of pursuers minimized. The pursuers are proven to intercept evaders successfully with the proposed optimal pursuit strategy. Several illustrative examples under two different cases are presented, and the results show that the cost of pursuers with the proposed target selection algorithm is the minimum of all results. [ABSTRACT FROM AUTHOR]

This paper investigates fully distributed scaled non-negative edge-consensus problems of networked systems with actuator saturation and unmeasurable internal states. By using the adaptive control method, output-feedback-based low-gain technique, and graph theory, a new adaptive algorithm is designed to obtain scaled edge-consensus conditions, under which the difficulties caused by the constraints on edge states and controllers are overcome. There are three interesting characteristics that any global information of networks is not used in this paper's algorithm and result, including the number of vertexes and edges; the feasible solutions of the scaled edge-consensus conditions exist and can be easily obtained; the convergence rate of the controller is adjustable. Furthermore, the designed algorithm is expanded in the cases without actuator saturation. Finally, three examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of input-to-state stability (ISS) of stochastic complex networks (SCNs). In this paper, an aperiodically intermittent control strategy based on sampled control is designed. By means of graph theory and Lyapunov method, two stability criteria on ISS are derived in this paper. After giving the estimate between E ∑ i = 1 m | x i (t) − x i (δ (t)) | 2 and E ∑ i = 1 m | x i (t) | 2 , a stability criterion is proposed on ISS of the SCN under aperiodically intermittent sampled control (AISC). When AISC degenerates into sampled control, another stability criterion on ISS of SCN is acquired. Finally, a numerical example is utilized to illustrate the effectiveness and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of stochastic mixed impulsive control and stability for stochastic functional differential systems with semi-Markov jump. A new definition of average stochastic impulsive gain is formulated to estimate the stochastic mixed impulsive intensity. Functional systems states are referred to the historical system states in the past time interval rather than in the past time instant of the current time instant. The stability analysis is carried out based on the constructed appropriate Lyapunov functional, Dupire functional Itô's formula, stochastic analysis theory and graph theory techniques. Moreover, we provide some exponential stability criteria for the investigated systems, which have close relation to not only the topological structures and semi-Markov jump of the functional systems but also average stochastic impulsive gain and stochastic disturbance intensity. Further we put it into practice of a new class of stochastic oscillators systems with semi-Markov jump and the corresponding numerical simulations results are on show to demonstrate the validity of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• The problem of graph Laplacian estimation with latent variables is formulated. • An multi-block ADMM algorithm is proposed to solve the problem. • The proposed method can estimate the conditional correlation of observed variables. In recent years, graph learning for smooth signals under Laplacian constraints has attracted increasing attention due to the wide application of graph Laplacian matrix in spectral graph theory, machine learning, and graph signal processing tasks. Standard graph learning methods usually assume that graphs are sparse, but the correlation between real-world entities is only sometimes sparse because of some common and potential effects. In this paper, we model these common effects as latent variables and assume that the Gaussian graphical model (GGM) under Laplacian constraints is conditionally sparse given latent variables but marginally non-sparse. Based on this assumption, the graph learning problem is formulated in a regularized maximum marginal likelihood (MML) framework with a sparse plus low-rank decomposition form. The specialized algorithm is developed to solve the proposed graph learning problem by incorporating Laplacian constraints into a multi-block alternating direction method of multipliers (ADMM) with proximal regularization terms. The experiments conducted on synthetic and real-world data sets demonstrate that the proposed graph learning method outperforms the standard method in inferring the sparsity pattern of the conditional graphical model of observed variables with the presence of latent variables. [ABSTRACT FROM AUTHOR]

Graph-based sparsity learning is one of the most successful unsupervised feature selection methods that has been widely adopted in many real-world applications. However, traditional graph-based unsupervised feature selection methods have several drawbacks: (1) being time-consuming and unable to deal with large-scale problems; (2) having difficulty tuning the regularization parameter with the sparsity regularization term; and (3) being unable to find explicit solutions owing to the limitation of sparsity, that is, feature selection with the ℓ 2 , 1 -norm constrained problem. Thus, this paper proposes OLPPFS, a method to preserve the local geometric structure within the feature subspace by imposing the ℓ 2 , 0 -norm constraint. First, the linear mapping capability of the proposed model is enhanced using locality-preserving projections (LPPs), whichpreserve the local and global geometric manifold structure of the data while enhancing the ability to reconstruct data. Second, the graph-embedding learning method can accelerate the construction of a sparsity affinity graph and describe the intrinsic structure of the dataset well. More importantly, we propose a method for solving a projection matrix with the ℓ 2 , 0 -norm constrained, which can accurately select a explicit group of discriminative feature subsets. This method can yield a more accurate sparse projection matrix than the ℓ 2 , 1 -norm. We also adopt FOLPPFS, an effective anchor-based strategy to further accelerate our model with two flexible options. Extensive experiments on eight datasets demonstrate that the proposed method is superior to the other methods and can preserve a better local geometric structure of the dataset with less time consumption. [ABSTRACT FROM AUTHOR]

• Distributed optimization problems of consensus are examined by a frequency-domain analysis approach. • An optimized distributed protocol is proposed such that the nonuniform time-delay FDMSs with SF have better consensus performance. • The double-integral dynamics of delayed FDMSs with SF is considered. This paper addresses distributed optimization problems concerning consensus in delayed fractional-order double-integrator multi-agent systems (FDMSs). To start with, an optimized distributed protocol with state-fractional-order-derivative feedback (SF) is presented for delayed FDMSs. Then, the consensus problems are studied for the two kinds of delayed FDMSs with SF in the presence of symmetric time-delays over undirected network topology and asymmetric time-delays over directed network topology. Next, by the means of graph theory, matrix theory and frequency-domain analysis method, the sufficient conditions to guarantee consensus of delayed FDMSs with SF are derived. Compared to the traditional distributed protocol without SF, the proposed distributed optimization protocol with SF are taken into account to enable better consensus performance in delayed FDMSs with SF. Finally, numerical experiments are carried out to verify the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time synchronization problem for switched neural networks with state-dependent switching under intermittent control is discussed. Different from previous literature, this paper uses aperiodically intermittent control to make switched neural networks achieve finite-time synchronization. A new differential inequality is established to get our main results. Meanwhile, based on graph theory and differential inclusions theory, a proper Lyapunov function is proposed to derive a criterion to ensure finite-time synchronization of switched neural networks. And the convergence time, closely related to the topological structure of networks, is obtained and does not rely on control widths or rest widths for aperiodically intermittent control. Finally, a numerical example is presented to illustrate the effectiveness and feasibility of our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results. [ABSTRACT FROM AUTHOR]

Graph theory analysis, as a mathematical tool, has been widely employed in studying the connectivity of the brain to explore the structural organization. Through the computation of graph theory metrics, it can effectively reveal the nonlinear and complex behavioral features of neuroimaging data, e.g., Electroencephalogram (EEG) and Magnetic Resonance Imaging (MRI), which are often challenging to interpret using simple linear methods. Graph neural networks (GNNs), employing deep learning, offer a more flexible approach to handling large-scale, high-dimensional brain network data. This review aims to investigate the applications of graph theory and Graph Neural Networks in the diagnosis of neurological disorders. The complexity and multi-level features of neurological disorders pose challenges for traditional methods in addressing such issues. The paper begins by introducing the fundamental principles of graph theory and GNNs, elucidates the mechanisms behind diagnosis process using these methods, and then provides a comprehensive overview of their specific applications. Finally, it discusses and summarizes the current challenges in this research field, proposing future directions for development. In conclusion, this review provides a thorough theoretical foundation and methodological insight for exploring the potential applications of graph theory and GNNs in the diagnosis of neurological disorders. ● This review explores GNNs and its variants in diagnosing neurological disorders using EEG and MRI data, analyzing gaps and improvements. ● The study highlights epilepsy research prevalence due to quality data and distinctive EEG patterns, noting GCN's dominant use and impact. ● The review calls for better data quality, GNN interpretability, and efficiency, promoting multi-disease diagnostics for personalized medicine. [ABSTRACT FROM AUTHOR]

The graph properties of r - and (r , s)-robustness are of importance for multiagent networks since these properties ensure consensus among agents even in the presence of a limited number of arbitrarily misbehaving agents, given sufficiently large values for the integers r and s. However, determining the exact solutions of r - and (r , s)-robustness of an arbitrary directed graph has been proven to be computationally complex NP-hard problem. In this paper, we introduce a novel method, named the Determining Robustness based Genetic Algorithm (DRSGA), for approximately calculating the r - and (r , s)-robustness using heuristic algorithm. According to graph theory in mathematical analysis, we first formalize the method for calculating the r - and (r , s)-robustness in directed graphs by utilizing a three-vertex set partition. Then, we transform these methods into a minimization problem of an n -dimensional discrete function and employ DRSGA to obtain an approximate solution. Finally, we validate the efficacy of our algorithm through a series of experiments compared to existing mixed-integer programming algorithms. [ABSTRACT FROM AUTHOR]

This paper concentrates on the bipartite finite-time consensus (BFTC) problem of nonlinear multi-agent systems (MASs) under intermittent communication via event-triggered impulsive control. First, a finite-time consensus (FTC) protocol with an event-triggered mechanism is developed for the MASs with nonlinear dynamics to save limited resources. Then, an impulsive control scheme is introduced to the designed algorithm to further improve the control performance. Based on the structurally balanced graph theory, both antagonistic and cooperative interactions are discussed in this article. Regarding whether the MASs have encountered intermittent communication, sufficient conditions are provided for achieving consensus of the MASs by using the Lyapunov theory and inductive methods. Moreover, the Zeno behavior is excluded. Finally, numerical simulations are given to validate the effectiveness of the algorithm. The result shows that the designed event-triggered BFTC control protocol with an impulsive strategy has a faster convergence rate than that without an impulsive strategy. [ABSTRACT FROM AUTHOR]

In this paper, the privacy-preserving-based bipartite consensus control problem is investigated for a class of discrete-time nonlinear multi-agent systems (MASs). The classical bipartite consensus control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents' private information, especially the initial states. Therefore, to prevent data disclosure to neighbors inside the MASs and the outside eavesdroppers, the data is encrypted by means of Paillier encryption scheme during information transmission. This means each agent first sends the relative data in the form of ciphertext to its neighbors for further encryption process, and then restores the control protocol based on the returned encrypted information from the neighbors. Since homomorphic encryption only works for integers, the data must be quantized before encryption, and it will inevitably result in the quantization error. On the other hand, for the purpose of saving communication resources, both decentralized and distributed event-triggered schemes are also proposed. Resorting to the Lyapunov stability theory and algebraic graph theory, sufficient conditions are derived ensuring that the MASs subject to a confidential communication agreement can achieve the bounded bipartite consensus. Two numerical examples are presented to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Highlights This paper studies the consensus problems for the two types of double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays: the DIFOMAS with symmetric time delays over undirected topology, and the DIFOMAS with asymmetric time delays over directed topology. The main contributions of this paper are as follows: • Consider the double-integrator fractional-order dynamics. • Consider the nonuniform time-delays, which contain up to n(n-1) different values when the DIFOMAS consists of n agents. • Consider the dynamics of each agent containing two state-variable with different fractional orders. • Obtain the two kinds of the upper bound of time-delays about Theorems 1 and 2 and the corollaries of Theorems 1 and 2. Abstract This paper addresses the distributed consensus control for a double-integrator fractional-order multi-agent system (DIFOMAS) with nonuniform time-delays. A general model of the DIFOMAS is introduced by such case: the dynamic model of each agent contains two state variables with different fractional orders. The consensus conditions on the two kinds of network topology and the nonuniform time-delays can be obtained by using the generic model: the DIFOMAS with symmetric time-delays over undirected topology, and the DIFOMAS with asymmetric time-delays over directed topology. With the help of matrix theory, Laplace transform and graph theory, two kinds of upper bounds of time-delays are derived to ensure the DIFOMAS with nonuniform time-delays can reach consensus. Finally, some numerical simulations with different parameters are offered to illustrate the feasibility and effectivity of the results derived. [ABSTRACT FROM AUTHOR]

Abstract Clustering analysis is to classify elements into categories based on their similarity. Clustering by fast search and find of density peaks (CFSFDP) has been proven to be an effective and novel algorithm, which identifies the centers of clusters with density maxima. However, the performance of CFSFDP is quite sensitive to the estimation of densities, that is exactly the selection of the cutoff distance (d c). In a conventional way, the selection of d c is based on subjective experience. It meets difficulties in finding an appropriate d c , especially for detecting nonspherical clusters, because CFSFDP cannot perform well when there are more than one density peak for one cluster. Besides, another barrier of applying CFSFDP is that manual interaction is always required for making an effective selection of cluster centers. In this paper, a new density-based clustering algorithm, clustering by defining and merging candidates of cluster centers via independence and affinity (CDMC-IA), is proposed. With its strategy, an appropriate value of cutoff distance d c can be well suggested and the robustness of the method itself is enhanced. Moreover, CDMC-IA introduces a new quantity independence to sort and select cluster centers, instead of human based selection from decision graph. Another quantity affinity is also introduced, which well handles multiple density peaks existing in one cluster and is able to assign each data point to the its targeted cluster. The performance of applying conventional clustering methods to benchmark datasets will be compared with the proposed method in this paper. [ABSTRACT FROM AUTHOR]

• An optimization problem about the state mean of multi-agent systems with impulsive noise based on MCC derived from information theoretic learning is investigated in this paper, where the half-quadratic(HQ) strategy is used to simplify the solving process of the optimization problem. • A problem interfered by impulsive noise on the states of multi-agent systems is studied in this paper, where the adverse effect of impulsive noise on the states is eliminated by the MCC algorithm. • An event-triggered consensus problem of discrete-time multi-agent systems with random impulsive noise is addressed in this paper, where an event-triggering condition is derived for the system to achieve consensus. An event-triggered consensus problem of discrete-time multi-agent systems with impulsive noise under directed switching topology is investigated in this paper, where the control input of each agent is determined by its own state information and the state information of its neighbors that may be corrupted by impulsive noise. Firstly, to reduce the adverse effect of impulsive noise on consensus performance of the discrete-time multi-agent systems, maximum correntropy criterion (MCC) derived from information theoretic learning is introduced to calculate the communication weights among the agents, and an event-triggered strategy is adopted to drive the state variables of each agent to eventually converge to a same value. Secondly, the condition to guarantee consensus of the discrete-time multi-agent systems is derived by graph theory and Lyapunov stability theorem. Finally, the effectiveness of the theory is verified by several numerical simulations. [ABSTRACT FROM AUTHOR]

Multiple Autonomous Underwater Vehicles (AUV) can complete complex ocean exploration missions cooperatively. This paper proposes a containment control algorithm under time-varying constraints by using a neural network for control of multiple benthic AUVs which are called the Ocean Bottom Flying Node (OBFN) systems. The multiple OBFNs in the presence of nonlinear model uncertainties are under the directed topology. First, we define the auxiliary variable and low-order filter. The anti-windup saturation auxiliary system is constructed in presence of the input saturation. Further, the adaptive law and neural network are designed to compensate environmental disturbances and systems model uncertainties, respectively. Moreover, in order to ensure the control performance of OBFN, an exponential boundary constraint is imposed which could constrain the system error convergent rates and bounds. Lyapunov stability theorem and graph theory are used to prove that the multiple OBFN systems are uniformly ultimately bounded. Finally, simulation results for multiple OBFNs illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization of stochastic coupled neural networks (SCNNs) with stochastic delayed impulses, which are more realistic and complex than the deterministic ones. Unlike previous works, we incorporate two distinct types of stochastic factors into the model: random noise affecting the systems continuous dynamics, and stochastic impulsive intensity applied at discrete impulsive instances. We extend the differential inequality with stochastic delayed impulses to stochastic systems without requiring that impulsive delay to be smaller than impulsive interval. We also model the impulsive intensity as a discrete-time Markov chain. By using the generalized inequality, graph theory, and stochastic analysis techniques, we derive a synchronization criterion for SCNNs with stochastic delayed impulses. We present numerical examples to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to develop an intelligent robot assembly system using multi-modal vision for next-generation industrial assembly. The system includes two phases where in the first phase human beings demonstrate assembly to robots and in the second phase robots detect objects, plan grasps, and assemble objects following human demonstration using AI searching. A notorious difficulty to implement such a system is the bad precision of 3D visual detection. This paper presents multi-modal approaches to overcome the difficulty: It uses AR markers in the teaching phase to detect human operation, and uses point clouds and geometric constraints in the robot execution phase to avoid unexpected occlusion and noises. The paper presents several experiments to examine the precision and correctness of the approaches. It demonstrates the applicability of the approaches by integrating them with graph model-based motion planning, and by executing the results on industrial robots in real-world scenarios. [ABSTRACT FROM AUTHOR]

With the development of hand-held photographic devices, document images in unconstrained environments can be captured in high-speed and high-resolution. It will be more efficient to process the text information of multiple documents simultaneously. In this paper, we propose a multi-document detection approach. It can estimate the amount of documents and also detect their accurate locations via iteratively searching the four corners and their direction maps from individual document in the image. Even for slightly occluded documents, the proposed method can infer the hidden corner positions. The model is designed to jointly learn the corner categories, locations and their directions in attentional regions via two branches of the same sequential prediction process. The association score is calculated based on the them between two corner connections. The graph theory, considering corners as nodes and association scores as edges, is applied to get the quadrangle for each document in image. For evaluation, we collect a Multi-Doc data set which contains 2,200 document images in various natural scenes. We show that the baseline model trained on this collected data and bench-mark SmartDoc 2015 can detect both single and multiple documents accurately and effectively. [ABSTRACT FROM AUTHOR]

This paper mainly studies the group consensus problem of the heterogeneous multi-agent systems with cooperative and competitive interactions and their strength among the agents. And both event-triggered mechanism and pinning control method are considered based on the system's topology with connected components. Besides, the novel fully distributed event-triggered conditions which only contain the local information for each agent are designed. Then, some sufficient conditions and the corresponding pinning control strategies are obtained via using algebraic graph theory and Lyapunov stability theorem, which can guarantee the system to reach multiple group consensus. In addition, Zeno-behavior for each agent is strictly excluded by utilizing time-correlation function. Finally, several simulations illustrate that our findings and the proposed methods are effective. Moreover, the results show that the convergence rate of the system will increase with the appropriate change of the cooperative or competitive interaction or their strength. [ABSTRACT FROM AUTHOR]

Both subspace learning methods and feature selection methods are often used for removing irrelative features from high-dimensional data. Studies have shown that feature selection methods have interpretation ability and subspace learning methods output stable performance. This paper proposes a new unsupervised feature selection by integrating a subspace learning method (i.e., Locality Preserving Projection (LPP)) into a new feature selection method (i.e., a sparse feature-level self-representation method), aim at simultaneously receiving stable performance and interpretation ability. Different from traditional sample-level self-representation where each sample is represented by all samples and has been popularly used in machine learning and computer vision. In this paper, we propose to represent each feature by its relevant features to conduct feature selection via devising a feature-level self-representation loss function plus an ℓ 2 , 1 -norm regularization term. Then we add a graph regularization term (i.e., LPP) into the resulting feature selection model to simultaneously conduct feature selection and subspace learning. The rationale of the LPP regularization term is that LPP preserves the original distribution of data after removing irrelative features. Finally, we conducted experiments on UCI data sets and other real data sets and the experimental results showed that the proposed approach outperformed all comparison algorithms. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the group consensus tracking issue of continuous-time second-order multi-agent systems (MASs) under directed fixed topology. A new protocol is introduced under the assumption that all the subgroups satisfy the in-degree balanced condition. For MASs with two subgroups, we first establish the relationship between the positive stability of matrix H and the connectedness of the topology graph. Then, we prove that MASs can achieve group consensus tracking if the system parameters satisfy some inequalities and matrix H is positive stable. Moreover, our paper extends the results for MASs with two subgroups to multiple χ -group consensus tracking. Especially, for a special graph with acyclic partition, a necessary and sufficient condition of χ -group consensus tracking is established. Finally, simulation examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of p th moment exponential stability for multi-links stochastic delayed complex networks with semi-Markov jump under hybrid multi-delay impulsive control. Different from the previous literature on multi-links systems, we take semi-Markov jump into account. The hybrid multi-delay impulses we addressed are composed of unstable delay-free impulses, stable delay-free impulses, unstable multi-delay impulses and stable multi-delay impulses. Average multi-delay impulsive gain is proposed to quantify the strength of the impulses. Serving as an extension of Halanay inequality, a novel multi-delay impulsive differential inequality is constructed. Combining the multi-delay impulsive differential inequality with Lyapunov method and graph theory, the sufficient criteria for p th moment exponential stability of the considered systems are given, which are closely related to average multi-delay impulsive gain, topological structure, stochastic disturbance strength and semi-Markov jump. Furthermore, the obtained theoretical results are applied to a class of stochastic delayed coupled oscillator systems. Finally, a corresponding numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Multi-group models have attracted considerable attention due to their promising potential applications in various fields. In this paper, aperiodically intermittent control is designed to study the exponential stability of fractional-order multi-group models with dispersal. By applying Lyapunov method and graph theory, some sufficient conditions about exponential stability are established. From the theoretical results, we observe that the convergence speed depends on the control gain and the order of fractional derivative. Moreover, to show the practicality of theoretical results, we provide an application of modified fractional-order competitive neural networks. A stability criterion is also given to guarantee the exponential stability of modified fractional-order competitive neural networks. Finally, a numerical example is provided to show the effectiveness of the stated results. Some simulation comparisons are also carried out to illustrate the relationship between the convergence speed and the control gain with the order of fractional derivative. [ABSTRACT FROM AUTHOR]

This paper proposes a graph feature selection method for dementia diagnosis, by adding the information inherent in the observations into a sparse multi-task learning framework. Specifically, this paper first defines two relations (i.e., the feature–feature relation and the sample–sample relation, respectively) based on the prior knowledge in the data. The feature–feature selection enforces the similarity relationship between features to be preserved in the coefficient matrix while the sample–sample relation is designed to preserve the relation between samples invariant in the predicted space. Then we embed these two kinds of relations into a multi-task learning framework (i.e., a least square loss function plus an l 2 -norm regularization term) to conduct feature selection. Furthermore, we feed the reduced data into Support Vector Machine (SVM) for conducting the identification of Alzheimer׳s Disease (AD). Finally, the experimental results on a subset of the Alzheimer׳s Disease Neuroimaging Initiative (ADNI) dataset showed the effectiveness of the proposed method in terms of classification accuracy, by comparing with the state-of-the-art methods, including k Nearest Neighbor ( k NN), ridge regression, SVM, and so on. [ABSTRACT FROM AUTHOR]

With the rapid accumulation of high dimensional data, dimensionality reduction plays a more and more important role in practical data processing and learning tasks. This paper studies semi-supervised dimensionality reduction using pairwise constraints. In this setting, domain knowledge is given in the form of pairwise constraints, which specifies whether a pair of instances belong to the same class (must-link constraint) or different classes (cannot-link constraint). In this paper, a novel semi-supervised dimensionality reduction method called Adaptive Semi-Supervised Dimensionality Reduction with Sparse Representation (ASSDR-SR) is proposed, which can get the optimized low dimensional representation of the original data by adaptively adjusting the weights of the pairwise constraints and simultaneously optimizing the graph construction using the ℓ 1 graph of sparse representation. Experiments on clustering and classification tasks show that ASSDR-SR is superior to some existing dimensionality reduction methods. [ABSTRACT FROM AUTHOR]

By resorting to a new matrix product, called semi-tensor product of matrices, this paper investigates the minimum stable set and core of graph, and also presents a number of results and algorithms. By defining a characteristic logical vector and using matrix expressions of logical functions, a new algebraic representation is derived for the externally stable set. Then, based on the algebraic representation, an algorithm is established to find all the externally stable sets. According to this algorithm, a new necessary and sufficient condition is obtained to determine whether a given vertex subset is an absolutely minimum externally stable set or not. Meanwhile, a new algorithm is also obtained to find all the absolutely minimum externally stable sets. Finally, the graph core, which is simultaneously externally stable set and internally stable set, is investigated. Here the internally stable set requires that internal nodes of this set are all disconnected with each other. Using semi-tensor product, some necessary and sufficient conditions are presented, and then an algorithm is established to find all the graph cores. The study of illustrative examples shows that the results/algorithms presented in this paper are effective. [ABSTRACT FROM AUTHOR]

Clustering ensemble is an important part of ensemble learning. It aims to study and integrate multiple clustering results from different clustering algorithms or same algorithm with different initial parameters for the same dataset. CHAMELEON is a hierarchical clustering algorithm which can discover natural clusters of different shapes and sizes as the result of its merging decision dynamically adapts to the different clustering model characterized. Inspired by the idea of CHAMELEON, the paper proposes a novel clustering ensemble models including semi-supervised method and discusses its application in fault diagnosis of high speed train (HST) running gear. The contributions of this paper include: constructing a sparse graph via the similarity matrix which aggregates multiple clustering results; partitioning the sparse graph (vertex=object, edge weight=similarity) into a large number of relatively small sub-clusters; obtaining the final clustering partition by merging these sub-clusters repeatedly. The experimental results demonstrate that our method outperforms some of state-of-the-art ensemble algorithms regarding the accuracy and stability and recognizes fault patterns of HST running gear effectively. [ABSTRACT FROM AUTHOR]

Recent advances in computational neuroscience have enabled trans-disciplinary researchers to address challenging tasks such as the identification and characterization of cognitive function in the brain. The application of graph theory has contributed to the modelling and understanding the brain dynamics. This paper presents a new approach based on a special graph theoretic concept called minimum connected component ( MCC ) to detect cognitive load induced changes in functional brain networks using EEG data. The results presented in this paper clearly demonstrate that the MCC based analysis of the functional brain networks derived from multi-channel EEG data is able to detect and quantify changes across the scalp in response to specific cognitive tasks. The MCC , due to its sensitivity to cognitive load, has the potential to be used as a tool not only to measure cognitive activity quantitatively, but also to detect cognitive impairment. [ABSTRACT FROM AUTHOR]

In this paper, delay-dependent-stability of stochastic delay coupled systems on networks with regime-switching-diffusions (SDCSRD) is investigated. Here, regime-switching-diffusions and time-varying delay are both considered into stochastic coupled systems on networks. Combining Lyapunov functional method with graph theory, several delay-dependent-stability criteria are derived to ensure H ∞ -stability and asymptotical stability in L p of SDCSRD. Particularly, as a concrete application of the theoretical results, we study the delay-dependent asymptotical stability in mean square of stochastic delay coupled oscillators with regime-switching-diffusions. Ultimately, two numerical examples are provided to exhibit the effectiveness of the results. [ABSTRACT FROM AUTHOR]

In order to bring the theoretical results into harmony or agreement with the reality, this paper copes with the leader-following mean square consensus issue for a class of nonlinear stochastic multi-agent systems with randomly occurring nonlinearities (RONs) and randomly occurring uncertainties (ROUs) under impulse time windows (ITWs). As a majorizing preconfigured mechanism of the windows, the configuration named periodically variable impulse time windows (PVITWs) is put forward. It not only ensures the periodic-based layout of impulse time window (ITW), but also allows the position and width of the window to be arbitrarily adjustable, so that the preset of ITW is more suitable for applications. Based on the Lyapunov stability theory and graph theory, the corresponding sufficient mean square consensus criteria are given. Finally, the feasibility of theoretical analysis is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronized stationary distribution of stochastic coupled networks with Markovian switching (CNMS) and the exponential synchronization of CNMS. Except for the Lyapunov method, the periodically intermittent control strategy and the technique of graph theory are applied to the study of synchronized stationary distribution and exponential synchronization. Some sufficient conditions to achieve synchronized stationary distribution and exponential synchronization are presented. The results show that the existing domain of synchronized stationary distribution is affected by control rate and the realization of exponential synchronization is also influenced by intensity of control, control rate. In addition, the theoretical results are applied to stochastic coupled oscillators and coupled Chua's circuits with Markovian switching. Finally, two examples with numerical simulations are provided to illustrate the effectiveness of the results developed. [ABSTRACT FROM AUTHOR]

Object tracking is a fundamental problem in computer vision. Although much progress has been made, object tracking is still a challenging problem as it entails learning an effective model to account for appearance change caused by intrinsic and extrinsic factors. To improve the reliability and effectiveness, this paper presents an approach that explores the combination of graph-based ranking and multiple feature representations for tracking. We construct multiple graph matrices with various types of visual features, and integrate the multiple graphs into a regularization framework to learn a ranking vector. In particular, the approach has exploited temporal consistency by adding a regularization term to constrain the difference between two weight vectors at adjacent frames. An effective iterative optimization scheme is also proposed in this paper. Experimental results on a variety of challenging video sequences show that the proposed algorithm performs favorably against the state-of-the-art visual tracking methods. [ABSTRACT FROM AUTHOR]

For multi-agent systems, significantly adding to the complexity of dynamical behaviors are intrinsic nonlinearity and stochastic noises due to environmental uncertainties. This paper deals with the mean square bounded consensus problem of multi-agent systems with intrinsic nonlinear dynamics, where each agent is affected by stochastic noises. Considering the impact of the former behaviors of nonlinear agents, we put forward a novel type of integral distributed delay protocol which is formed as a weighted sum of historical information exchange over all time interval [ t − τ , t ] . Compared with the previous work, the protocol expression of this paper is more general and includes many traditional protocols as its special cases. Based on a Lyapunov-based approach, together with results from matrix theory and algebraic graph theory, sufficient conditions are derived for the mean square bounded consensus. Simulation examples with nonlinear even chaotic agents illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The cooperative exponential synchronization of multi-agent chaotic delayed neural networks (DNNs) with switching topology, stochastic disturbance and impulsive disturbance is investigated in this paper. Based on the Lyapunov stability theory, algebraic graph theory, matrix theory and the helpful stochastic Halanay inequality technique, some sufficient conditions are presented to guarantee the cooperative exponential synchronization for multi-agent chaotic DNNs with switching topology. Compared with the existing works about synchronization (or consensus) of multi-agent systems, the proposed method in this paper can provide a more general framework for the cooperative synchronization of nonlinear multi-agent systems with or without time delays, stochastic and impulsive disturbances. The famous master–slave (drive-response) synchronization of chaotic DNNs is a special case of this paper, and therefore the derived results can also be favorable for practical application in secure communication. Simulation results finally verify the effectiveness of the proposed synchronization control algorithm. [ABSTRACT FROM AUTHOR]

In this contribution, we aim to examine the scaled consensus problem for heterogeneous multi-agent systems, which comprise two kinds of agents: the agents with first-order dynamics and the agents with second-order dynamics. The scaled consensus here means that the ratios between the states of the agents asymptotically approach specified constants instead of the same value. Firstly, appropriate distributed control protocols are designed for first-order and second-order networked agents, respectively. Particularly, the effects of switching communication networks and time-varying delays on model performance are investigated in this paper. Secondly, an augmented system approach based on algebraic graph theory and non-negative matrix theory is adopted to solve the proposed scaled consensus problem. Finally, a sufficient criterion is established to certify the scaled consensus performance of mixed agents. The correctness of the theoretical result is demonstrated through several simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of group consensus for a novel network model, which possesses a two-layer structure and consists of multiple interactive agents. Agents in the network are divided into several different groups according to hybrid interactions, then two neighboring agents can belong to the same group, different groups but in the same layer or different layers. Correspondingly, three kinds of relationships exist between neighboring agents in the network. Furthermore, consider that only agents in the first layer are pinned by virtual leaders, then based on the graph theory, Lyapunov function method, and optimization technique, some criteria for realizing group consensus of the network under fixed topology and switching topologies are established, which mainly depend on the topology and time intervals of the switching signal. It is found out that when the group consensus is achieved, the agents in the first layer follow the leaders asymptotically, while the agents in the second layer converge to opposite states of the leaders. Finally, a detailed numerical example is given for illustration. [ABSTRACT FROM AUTHOR]

This paper explores stability of new fractional-order impulsive coupled (FOIC) non-autonomous systems on networks. By utilizing graph theory and structuring individual vertex's Lyapunov function, a systematic method is present to construct global Lyapunov functions of FOIC systems. By Lyapunov method, a new inequality as well as the graph theory, several new stable principles are derived based on the strongly connected property. Besides, several more general criteria are obtained by utilizing these principles to the FOIC systems, including uniform stability, exponential stability and Mittag-Leffler stability for a kind of FOIC systems. At last, a numerical example is provided to show the effectiveness of our findings. [ABSTRACT FROM AUTHOR]

The paper addresses a distributed containment issue for a stochastic nonlinear strict-feedback multi-agent system. In combination with the graph theory and neural networks technique, an adaptive neural containment protocol is developed within the traditional backstepping framework. Such a containment protocol allows one to extend some existing results to the case that multiple followers are confined to stochastic nonlinear dynamics. Furthermore, with the help of the quartic Lyapunov function, it is proved that all the signals in the resulting closed-loop system remain bounded in probability and the containment error converges to a small neighborhood of the origin in the sense of mean square by a suitable choice of parameters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

The paper is concerned with the p th moment exponential synchronization for stochastic Markovian switching complex networks with multi-links via aperiodically intermittent control. Different from the current literature on multi-links systems, the networks we consider have time-varying topology structure. New differential inequalities are established in which the Markovian switching and multiple time-varying delays are taken into account and the constraint on parameter that determines exponential convergence rate is reduced. Based on Lyapunov method, graph theory and differential inequality techniques, some sufficient conditions are obtained to achieve exponential synchronization. As a result, the developed synchronization criteria have more accurate exponential convergence rate than that in most existing literature which focuses on delayed systems with intermittent control. Finally, an application to modified Chua's circuits and corresponding numerical simulations are presented to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, formation control problem for multiple uncertain nonlinear second-order agents in the presence of heterogeneous communication delays is addressed. A continuous repulsive vector is incorporated into agents' velocity to ensure collision avoidance, whose time derivative is approximated via a finite-time robust integral of the sign of the error (RISE)-like observer. Using adaptive neural control scheme, unknown model dynamics, external disturbances, RISE estimation error, and the time-delays among agents are robustly addressed. The sufficient conditions on the stability of the overall system and collision avoidance are derived using Lyapunov–Krasovskii functionals and algebraic graph theory, and it is proven that the formation tracking error converges to a small neighborhood of zero. Numerical simulation results are also given to illustrate the effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

Throughout this paper, the stabilization problem of random coupled systems on networks with Markovian switching (RCSNMS) is considered via aperiodically intermittent control. It is worth noting that aperiodically intermittent control is firstly utilized to stabilize random systems which are derived by more general noise. On the basis of Lyapunov method, graph theory together with some new stochastic analysis techniques, several stability criteria are derived. Different from most existing stability results on random systems in the literature which are mainly noise-to-state stability, we consider global asymptotical stability in probability and exponential stability in p th moment of RCSNMS. Then an application of the obtained results for a class of random coupled oscillators with Markovian switching via aperiodically intermittent control is presented. Finally, two numerical examples are concerned to demonstrate the validity and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization problem of complex-valued delayed coupled systems on networks with aperiodically on-off coupling is investigated. The on-off coupling is aperiodic, which takes the general on-off coupling as a special case. We analyze the complex-valued system directly by using R -Derivative and Conjugate R -Derivative. Then based on the Lyapunov method and graph theory, we give two kinds of synchronization criteria, which have a close relationship with the switch-on width of the coupling and the topological structure of the underlying network. Specially, when the switch-on width tends to zero, on-off coupling becomes impulsive control. Hence, the corresponding synchronization criteria under impulsive control are given as well. To illustrate the practicability of the main results, we apply the derived results to complex-valued delayed coupled oscillators. Finally, two numerical examples are given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: Gaussian processes are a popular and effective Bayesian method for classification and regression. Due to the cube time complexity with respect to the size of the training set, time consumption will be too high for Gaussian processes to deal with big data sets. Based on the manifold assumption, manifold-preserving graph reduction (MPGR) is a simple and efficient graph sparsification method originally proposed for sparse semi-supervised learning. High representative points are selected, while outliers and noisy points are excluded by MPGR with low time consumption. In this paper, we apply MPGR to sparse supervised learning, and utilize MPGR to get a sparse representation of Gaussian processes. A fatal shortcoming of MPGR is that it does not effectively consider the influence of outputs to Gaussian processes. We proceed to exploit outputs for sparse Gaussian processes by embedding a method that considers outputs in the MPGR framework, and propose manifold-preserving graph reduction with outputs (MPGRO) for sparse Gaussian processes. In this paper, we utilize informative vector machine (IVM) for MPGRO. Experimental results on seven real data sets show that MPGR is better than IVM for sparse Gaussian processes, and MPGRO is better than MPGR and IVM for sparse Gaussian processes and is comparable on error rates to the method utilizing full training sets. [Copyright &y& Elsevier]

Abstract: Graph-based semi-supervised learning has been widely researched in recent years. A novel Low-Rank Representation with Local Constraint (LRRLC) approach for graph construction is proposed in this paper. The LRRLC is derived from the original Low-Rank Representation (LRR) algorithm by incorporating the local information of data. Rank constraint has the capacity to capture the global structure of data. Therefore, LRRLC is able to capture both the global structure by LRR and the local structure by the locally constrained regularization term simultaneously. The regularization term is induced by the locality assumption that similar samples have large similarity coefficients. The measurement of similarity among all samples is obtained by LRR in this paper. Considering the non-negativity restriction of the coefficients in physical interpretation, the regularization term can be written as a weighted -norm. Then a semi-supervised learning framework based on local and global consistency is used for the classification task. Experimental results show that the LRRLC algorithm provides better representation of data structure and achieves higher classification accuracy in comparison with the state-of-the-art graphs on real face and digit databases. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a system for face identification. Given two query face images, our task is to tell whether or not they are of the same person. The main contribution of this paper comes from two aspects: (1) We adopt the one-shot similarity kernel [35] for learning the similarity of two face images. The learned similarity measures are then used to map a face image to reference images. (2) We propose a graph-based method for selecting an optimal set of reference images. Instead of directly working on the image features, we use the learned similarity to the reference images as the new features and compute the corresponding matching score of the two query images. Our approach is effective and easy to implement. We show encouraging and favorable results on the “Labeled Faces in the Wild” – a challenging data set of faces. [Copyright &y& Elsevier]

Abstract: In this paper, a novel semi-supervised learning approach is proposed. It assumes that, for the ith sample , the samples from ''s sparse neighborhood have the same label with and the label of can be linearly reconstructed by the labels of those samples from ''s sparse neighborhood. Our algorithm firstly selects the sparse neighborhood for each sample, and then in that sparse neighborhood finds the sparse coefficients to represent the local geometry structure, finally seeks a label propagation way. Different from many existing methods, we construct the adapting graph, simultaneously, give the weight of each edge. What''s more, we highlight the role of those samples in that sparse neighborhood, meanwhile, eliminate the role of those samples out of that sparse neighborhood. The experimental results on face recognition and document classification demonstrate the effectiveness and efficiency of our proposed approach in this paper. [Copyright &y& Elsevier]

This paper focuses on the global synchronization problem for two fractional-order complex networks with non-delayed and delayed coupling (FCNNDC) by using hybrid impulsive control strategy. First, a fractional-order comparison principle is established firstly. Based on our proposed comparison principle and combining algebraic graph theory and laplace transform as well as mathematical induction, some novel synchronization criteria revealing the interplay among the impulsive gain, impulsive interval, networks' topology structure and fractional order, are derived to guarantee the global synchronization of FCNNDC. Finally, some numerical results are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]