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Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets.

This work deals with the problem of passivity analysis of fractional-order neural networks (FONNs) with impulse, proportional delays and state-dependent switching parameters. The novelty of the work lies in addressing the crucial issue of developing a delay-dependent LMI condition for analysing the behaviour of delayed FONNs. In this paper, a new lemma on Caputo fractional derivatives is developed to construct a new Lyapunov functional to derive delay dependent LMI condition for the passivity analysis of FONNs. Besides that, under modification, another sufficient condition is derived to give an impulse gain-dependent LMI condition. Moreover, for the first time in the literature, delay-dependent and order-dependent passivity criteria for fractional-order systems with proportional delays are presented in this paper. Finally, the results obtained are verified with suitable numerical parameter values and the simulation results are demonstrated to show the effectiveness of the proposed method and superiority of FONNs.

In this paper, the multiple asymptotic stability is investigated for fractional-order quaternion-valued neural networks (FQVNNs) with time-varying delays. The activation function is a nonmonotonic piecewise nonlinear activation function. By applying the Hamilton rules, the FQVNNs are transformed into real-valued systems. Then, according to the Brouwer’s fixed point theorem, three new conditions are proposed to ensure that there exist 3 4 n equilibrium points. Moreover, by virtue of fractional-order Razumikhin theorem and Lyapunov function, a new condition is derived to guarantee the FQVNNs have 2 4 n locally asymptotic stable equilibrium points. For the first time, the multiple asymptotic stability of delayed FQVNNs is investigated. Contrast to multistability analysis of integer-order quaternion-valued neural networks, this paper present different conclusions. Finally, two numerical simulations demonstrate the validity of the results.

In this paper, the asymptotic stability of static neural networks with interval time-varying delay is studied. An improved integral inequality based on orthogonal polynomials is proposed, in which three free vectors can be selected independently. A novel Lyapunov–Krasovskii functional containing more delayed state information, instant state information and integrated state information is constructed. Based on the improved non-convex technique, two less conservative delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are derived. The validity and superiority of the theoretical results derived in this paper are verified by numerical simulation.

This paper investigates the multistability on a class of delayed neural networks with monotonically nondecreasing linear activation function. For n state neurons with 2 m + 1 piecewise linear activation function, we prove the neural networks have ( 2 m + 1 ) n equilibrium points, ( m + 1 ) n of which are locally exponentially stable. Different from the traditional multistability analysis method such as fixed point theory, this paper only uses the character of activation functions, and can also handle the neural networks with disturbance term. The research results of this paper generalize the previous related research works and are easy to test. A numerical example is given to shown the effectiveness of our theoretical results.

This paper addresses the global exponential stability of a class of quaternion-valued neural networks (QVNNs) with mixed delays including time-varying delays and infinite distributed delays. Because of the noncommutativity of quaternion multiplication, the concerned quaternion-valued models separated into four real-valued parts to form the equivalent real-valued systems. Based on M-matrix properties and homomorphism mapping theories, some sufficient conditions are derived to guarantee the existence and uniqueness of the equilibrium point of the system. Conditions for ensuring the global exponential stability of the equilibrium point of the system are obtained on the basis of the vector Lyapunov function method instead of the linear matrix inequality method. Using a similar method, the mixed-delay QVNNs with parameter uncertainties are also studied, and the conditions for ensuring the global robust exponential stability of the system are established directly. The adopted approach and the obtained results in this paper complement already the existing ones. Finally, three numerical examples are provided to illustrate the feasibility and the less level conservatism of the main results.

In this paper, the robust stability of uncertain fractional order singular systems with neutral and time-varying delays is investigated. By applying Lyapunov–Krasovskii functional approach, several sufficient conditions in the form of linear matrix inequality to ensure asymptotical stability and robust stability are derived for the considered systems. The advantage of the employed method in this paper is that one may directly calculate integer-order derivatives of Lyapunov–Krasovskii functional. Several simple examples are given to illustrate the effectiveness of the obtained results.

This paper studies the exponential stability problem of neural networks with a time-varying delay. Firstly, an augmented Lyapunov-Krasovskii functional (LKF) containing a single integral state is constructed. Then a generalized free-matrix-based integral inequality and the auxiliary function-based integral inequality combined with an extended reciprocally convex matrix inequality are used to estimate the derivative of the LKF. The novelty of this paper is that some state-dependent zero equations are introduced into before and after bounding the LKF’s derivative so as to increase the freedom and reduce the conservatism. As a result, a less conservative stability criterion is derived in the form of linear matrix inequality, whose superiority is illustrated with three numerical examples.

In this paper, the non-fragile dissipative filtering problem is investigated for the two-dimensional (2-D) systems subjected to randomly occurring uncertainties and redundant channel protocol. For the redundant channel transmission, if a signal fails to be transmitted through a certain channel, the next channel is immediately activated to transmit the signal once again. The norm-bounded uncertainties are introduced in the considered system, which are governed by two stochastic variables obeying the Bernoulli distribution law. The aim of this paper is to design a dissipative filter in a non-fragile manner such that the augmented filtering error system is not only asymptotically stable in the mean-square sense but also satisfies a strict 2-D ( Q , S , R ) − α -dissipativity performance index. Based on the Lyapunov theory and stochastic analysis, sufficient conditions are first given to guarantee the asymptotic stability of the 2-D system in the mean-square sense. Then, the non-fragile filter is designed to ensure that the 2-D system satisfies the strict 2-D ( Q , S , R ) − α -dissipativity performance index, under which the expressions of the non-fragile filter gains are given by solving certain matrix inequalities. Finally, a simulation example is provided to show the effectiveness of the proposed dissipative filtering method.

In this paper, some new p-stability criteria and boundedness results of reaction–diffusion BAM neural networks are derived by way of fixed point theorem, Laplacian semigroup theory and L∞-estimate technique, which are novel against those of the previous related literature. Since the T–S fuzzy impulsive reaction–diffusion neural networks was investigated by previous literature, the main difficulty of this paper is to find out a novel method to give simpler conclusions than existing results. Finally, a numerical example is presented to illustrate the effectiveness and feasibility of the proposed methods.

Firstly, a general tridiagonal two-layer neural network model with 2n-neuron is proposed, where every layer has time delay. A new method of Hopf bifurcation analysis is introduced by matrix decomposition in this paper. Through factoring the tridiagonal matrix, the characteristic equation of the neural network model is simplified. Secondly, by studying the eigenvalue equations of the related linear system for the special six-neuron (three neurons per layer) two-layer neural network model, the sufficient conditions for experiencing the Hopf bifurcation are obtained. The conditions obtained by the new method proposed in this paper are simpler and more practical than those obtained by the traditional Hurwitz discriminant method. Next, based on the normal form method and the center manifold theorem, the explicit formulae about the stability of the bifurcating periodic solution and the direction of the Hopf bifurcation are established. Finally, the main results obtained in this paper are illustrated by three numerical simulation examples.

This paper addresses the problem of establishing the asymptotic stability criteria for genetic regulatory networks with discrete time delays. First, the system model is simplified to a reduced-order system with bounded uncertain parameters and distributed delays by exploiting calculus’s properties and Lagrange’s mean–value theorem. Second, the relationship between the asymptotic stability of the primal system and the robust asymptotic stability of the reduced-order one is investigated. Third, a new reduced-order approach is proposed to derive a sufficient condition for the robust asymptotic stability of the reduced-order system (i.e., the asymptotic stability of the primal system). At last, a numerical example illustrates the effectiveness of the theoretical results obtained in this paper.

Independent component analysis (ICA) is a standard method for separating a multivariate signal into additive components that are non-Gaussian and independent from each other. This paper introduced a novel algorithm to perform ICA employing matrix exponentials, which performs similarly to geodesic based methods but based on a different insight. First, we showed that the ICA problem can be formulated as an optimization problem in the space of orthogonal matrices whose determinants are one, which can be further transformed into an equivalent problem in the space of antisymmetric matrices. Then, an efficient approach was presented for iteratively solving this problem using the antisymmetric matrices with one or more nonzero columns and rows. Especially, we proved that in the sense of local optimization it is sufficient to employ antisymmetric matrices with only one nonzero column and row. The analytical expressions of exponentials of such special antisymmetric matrices were also explicitly established in this paper. Compared to other competing algorithms, experimental results indicated that the proposed method can achieve separation with superior performance in term of the precision and running speed.

In this paper, by employing fixed point theorem, generalized Gronwall–Bellman inequality and differential inequality techniques, some sufficient conditions are given for the existence and the exponential stability of the unique piecewise weighted pseudo almost-periodic solution of impulsive high-order recurrent neural networks with time-varying coefficients and mixed delays. An illustrative example is also given in the end of this paper to show the effectiveness of our results.

In this paper, a new approach based on least squares support vector machines (LS-SVM) is proposed for solving the electromagnetic equations. Firstly, the cubic spline function is employed to smooth the discontinuous boundary. LS-SVM is used to solve the modified problem. Secondly, nonlinear electromagnetic equation is solved by LS-SVM. Finally, multimedia electromagnetic equation is solved by LS-SVM. Same as to the artificial neural networks (ANN), the approximate solutions are composed of two parts. The first part is a known function that satisfies the boundary conditions. The second part is the product of two terms. One term is also a known function which vanished on the boundary. The left part is the combination of kernel functions containing regression parameters. The parameters can be obtained by solving a system of equations. The numerical results show that the proposed method in this paper is feasible.

The paper is concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed complex-valued Cohen–Grossberg neural networks. Without using the method of the a priori estimate of periodic solutions, by combining Mawhin’s continuation theorem of coincidence degree theory with LMI method and using inequality techniques, a novel LMI-based sufficient condition on the existence of periodic solutions is established for the complex-valued Cohen–Grossberg neural networks. Then by using inequality techniques, a novel sufficient condition on the global asymptotic stability of periodic solutions for the above complex-valued neural networks is established. Our results and method are new and complementary to the existing papers on the study of periodic solutions of neural networks.

Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. Examples are Gaussian RBF kernels, kernel learning, and hierarchical Gaussian kernels which were recently proposed for deep learning. Therefore, the actually used kernel is often computed by a grid search or in an iterative manner and can often only be considered as an approximation to the “ideal” or “optimal” kernel. The paper gives conditions under which classical kernel based methods based on a convex Lipschitz loss function and on a bounded and smooth kernel are stable, if the probability measure P, the regularization parameter λ, and the kernel K may slightly change in a simultaneous manner. Similar results are also given for pairwise learning. Therefore, the topic of this paper is somewhat more general than in classical robust statistics, where usually only the influence of small perturbations of the probability measure P on the estimated function is considered.

The sign dynamical system for unconstrained minimization of a continuously differentiable function f is examined in this paper. This dynamical system has a discontinuous right hand side and it is interpreted here as neural network. Asymptotic convergence is proven (by using Filippov's approach) finite-time convergence of its solutions is established and an improved upper bound for convergence time is given. A first contribution of this paper is a detailed calculation of Filippov set-valued map for the sign dynamical system, in the general case, i.e. without any restrictive assumptions on the function f to be minimized. Convergence of its solutions to stationary points of f follows by using standard results, i.e. a generalized version of LaSalle's invariance principle. Next, in order to prove finite-time convergence of solutions, the applicability of standard results is extended so that they can be applied to the sign dynamical system. Finally, while establishing finite-time convergence, a novel proving procedure is introduced which (i) allows for milder assumptions to be made on the function f, and (ii) results in an improved upper bound for the convergence time. Numerical experiments confirm both the effectiveness and finite-time convergence of the sign neural network.

Being motivated by combining the advantages of hyperplane-based pattern analysis and fuzzy clustering techniques, we present in this paper a fuzzy mix-prototype (FMP) clustering for microarray data analysis. By integrating spherical and hyper-planar cluster prototypes, the FMP is capable of capturing latent data models with both spherical and non-spherical geometric structures. Our contributions of the paper can be summarized into three folds: first, the objective function of the FMP is formulated. Second, an iterative solution which minimizes the objective function under given constraints is derived. Third, the effectiveness of the proposed FMP is demonstrated through experiments on yeast and leukemia data sets.

This paper investigates the stability analysis and observer-based controllers design for T–S fuzzy positive systems. A fuzzy copositive Lyapunov function is first proposed to analyze the stability of the T–S fuzzy positive systems via linear programming. In terms of the property of the fuzzy membership functions, the fuzzy copositive Lyapunov function is employed to derive the less conservative stability conditions. Then, the line-integral Lyapunov function is presented for the stability analysis. The time-derivatives of the membership functions do not appear in the stability analysis of the T–S fuzzy positive systems, therefore, the proposed stability conditions are more relaxed than those of the conventional Lyapunov function approaches. Based on the obtained stability conditions, observer-based control schemes are designed such that the resultant closed-loop systems are both stable and positive. Finally, two examples are provided to validate the effectiveness of the results proposed in this paper.

This paper studies the finite-time synchronization problem of nonlinear complex dynamical networks (NCDNs) on time scales. A pinning impulsive control strategy, in which only a small portion of nodes are impulsively controlled, is designed to achieve finite-time synchronization for NCDNs on time scales. Based on the theory of time scales, Lyapunov method and mathematical induction approach, a finite-time synchronization criterion is obtained for NCDNs on time scales under the pinning impulsive control strategy. It is shown that the finite-time synchronization criterion in this paper is different from that derived for continuous-time or discrete-time NCDNs. Moreover, the idea of this paper provides a unified approach to study the finite-time synchronization problems for continuous-time NCDNs and their discrete-time counterparts simultaneously. A numerical simulation example is given to illustrate the effectiveness of our result.

This paper discusses the classifier ensemble problem with sparsity and diversity learning, which is a central issue in machine learning. The current approach for reducing the size and increasing the accuracy of a classifier ensemble is to formulate it as a convex quadratic programming problem, which is a relaxation problem, and then solve it by using the existing methods for convex quadratic programming or by computing closed-form solutions. This paper presents a novel computational approach for solving the classifier ensemble problem with sparsity and diversity learning without any recourse to relaxation problems and their associated methods. We first show that the classifier ensemble problem can be expressed as a minimization problem for the sum of certain convex functions over the intersection of fixed point sets of quasi-nonexpansive mappings. Next, we propose fixed point optimization algorithms for solving the minimization problem and show that the algorithms converge to the solution of the minimization problem. It is shown that the proposed algorithms can directly solve the classifier ensemble problem with sparsity and diversity learning. Finally, we compare the performance of the proposed sparsity and diversity learning methods against an existing method in classification experiments using data sets from the UCI machine learning repository and the LIBSVM. The experimental results show that the proposed methods have higher classification accuracies than the existing method.

This paper proposes a valid and fast algorithm for low-rank matrix factorization. There are multiple applications for low-rank matrix factorization, and numerous algorithms have been developed to solve this problem. However, many algorithms do not use rank directly; instead, they minimize a nuclear norm by using Singular Value Decomposition (SVD), which requires a huge time cost. In addition, these algorithms often fix the dimension of the factorized matrix, meaning that one must first find an optimum dimension for the factorized matrix in order to obtain a solution. Unfortunately, the optimum dimension is unknown in many practical problems, such as matrix completion and recommender systems. Therefore, it is necessary to develop a faster algorithm that can also estimate the optimum dimension. In this paper, we use the Hidden Matrix Factorized Augmented Lagrangian Method to solve low-rank matrix factorizations. We also add a tool to dynamically estimate the optimum dimension and adjust it while simultaneously running the algorithm. Additionally, in the era of Big Data, there will be more and more large, sparse data. In face of such highly sparse data, our algorithm has the potential to be more effective than other algorithms. We applied it to some practical problems, e.g. Low-Rank Representation(LRR), and matrix completion with constraint. In numerical experiments, it has performed well when applied to both synthetic data and real-world data.

In this paper, we put in effort to inspect the passivity and exponential passivity problem of memristive neural networks with time-varying delays and reaction–diffusion term. Based on the basis of generalized Lyapunov approach, Poincar e ` inequality, Schur complement Lemma, free-weighting matrix approach as well as some inequality techniques, the main conclusions of this paper are derived in the form of linear matrix inequality (LMI). What is noteworthy is that the obtained sufficient criteria rely on the reaction–diffusion term, which implies that the reaction–diffusion term can effect the passivity of the given system. Finally, two numerical examples are emerged to check the practicability of the derived passivity conditions.

In this paper, we propose a new filtering framework called discriminatively guided image filtering (DGF), for hyperspectral image (HSI) classification. DGF integrates a discriminative classifier and a generative classifier by the guided filtering (GF), considering the complementary strength of these two types of classification paradigms. To demonstrate the effectiveness of the proposed framework, the combination of support vector machine (SVM) and linear discriminative analysis (LDA), which serve as a discriminative classifier and a generative classifier respectively, is investigated in this paper. Specifically, the original HSI is projected into the low-dimensional space induced by LDA to serve as guidance images for filtering the intermediate classification results induced by SVM. Experiment results show the superior performance of the proposed DGF compared with that of the principal component analysis (PCA)-based GF.

The problem of subspace clustering which refers to segmenting a collection of data samples approximately drawn from a union of linear subspaces is considered in this paper. Among existing subspace clustering algorithms, low rank representation (LRR) based subspace clustering is a very powerful method and has demonstrated that its performance is good. Latent low rank representation (LLRR) subspace clustering algorithm is an improvement of the original LRR algorithm when the observed data samples are insufficient. The clustering accuracy of LLRR is higher than that of LRR. Recently, Frobenius norm minimization based LRR algorithm has been proposed and its clustering accuracy is higher than that of LRR demonstrating the effectiveness of Frobenius norm as another convex surrogate of the rank function. Combining LLRR and Frobenius norm, a new low rank representation subspace clustering algorithm is proposed in this paper. The nuclear norm in the LLRR algorithm is replaced by the Frobenius norm. The resulting optimization problem is solved via alternating direction method of multipliers (ADMM). Experimental results show that compared with LRR, LLRR and several other state-of-the-art subspace clustering algorithms, the proposed algorithm can get higher clustering accuracy. Compared with LLRR, the running time of the proposed algorithm is reduced significantly.

This paper deals with a class of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator. Using the differential inequality theory and Lyapunov functional method, a set of sufficient conditions which ascertains that the existence and exponential stability of anti-periodic solutions of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator are derived. Computer simulations are delineated to substantiate the correctness of our theoretical predictions. The obtained results of this paper are new and complement some earlier works.

An algorithm that generates an exponential number of stable states for the very well-known Hopfield Neural Network (HNN) is introduced in this paper. We show that the quantity of stable states depends on the dimension and number of components of the input pattern supporting noise. Extensive tests verify that the states generated by our algorithm are stable states and show the exponential storage capacity of a HNN. This paper opens the possibility of designing improved HNNs able to achieve exponential storage, and thus find their applicability in complex real-world problems.

In this brief paper, a membership function dependent Lyapunov–Krasovskii functional is designed to investigate the stability analysis of T–S (Takagi–Sugeno) fuzzy systems with time delay. According to the time derivatives of the membership function, both local and global stability conditions are obtained. For the local case, the local stability region is obtained by designing an algorithm. In the end, an example is given to illustrate the effectiveness of the method in this paper.

In this paper, we introduce taxonomies for similarity and dissimilarity measures, respectively, based on their mathematical properties. Further, we propose a definition for rank equivalence of (dis)similarities regarding given data for prototype based methods. Starting with this definition we provide a measure to judge the degree of equivalence, which can be used to compare respective measures as well as to consider the influence of data preprocessing regarding a single (dis)similarity measure. In the last part of the paper an adaptive mixture approach of (dis)similarity measures for improved classification learning is presented.

In this paper, the discrete-time quaternion-valued neural network with linear threshold activation functions is investigated. The sufficient conditions to the boundedness and global exponential periodicity of the neural network are obtained by using characteristic equation, Lyapunov functional and M -matrix. Simulation results illustrative the effectiveness of the conclusions obtained in this paper.

Interval-valued data arises in situations where it is needed to manage either the uncertainty related to measurements, or the variability inherent to a group rather than an individual. This paper proposes a fuzzy c-means clustering algorithm based on suitable adaptive City-Block and Hausdorff distances with the purpose to cluster interval-valued data. This fuzzy c-means clustering algorithm optimizes explicitly an objective function by alternating three steps aiming to compute the fuzzy cluster representatives, the fuzzy partition, as well as relevance weights for the interval-valued variables. Indeed, most often conventional fuzzy c-means clustering algorithms consider that all variables are equally important for the clustering task. However, in real situations, some variables may be more or less important or even irrelevant for clustering. Due to the use of adaptive City-Block and Hausdorff distances, the paper proposes a fuzzy c-means clustering algorithm that tackles this problem with a step where a relevance weight is automatically learned for each interval-valued variable. Additionally, various tools for the fuzzy partition and fuzzy cluster interpretation of interval-valued data provided by this algorithm is also presented. Experiments with suitable synthetic and real interval-valued datasets demonstrate the robustness and the usefulness of this fuzzy c-means clustering algorithm and the merit of the fuzzy partition and fuzzy cluster interpretation tools.

The problem of choosing error penalty parameter C for optimization extreme learning machine (OELM) is that it can take any positive value for different applications and it is therefore hard to choose correctly. In this paper, we reformulated OELM to take a new regularization parameter ν (ν-OELM) which is inspired by Scholkopf et al. The regularization in terms of ν is bounded between 0 and 1, and is easier to interpret as compared to C. This paper shows that: (1) ν-OELM and ν-SVM have similar dual optimization formulation, but ν-OELM has less optimization constraints due to its special capability of class separation and (2) experiment results on both artificial and real binary classification problems show that ν-OELM tends to achieve better generalization performance than ν-SVM, OELM and other popular machine learning approaches, and it is computationally efficient on high dimension data sets. Additionally, the optimal parameter ν in ν-OELM can be easily selected from few candidates.

This paper investigates the sampled-data state estimation problem for a class of delayed complex networks. At certain sampling times, transmission of sampled-data through communication network may fail, which means the considered estimator can only intermittently receive sampled-data. The main objective of this paper is to design a sampled-data state estimator subjected to intermittent transmission such that the error system is exponentially stable. Specifically, the error system is first transformed into time-varying delayed switched systems, including both stable and unstable subsystems. And then, to analyze the stability of the error system, a modified Halanay inequality is presented. In view of the modified Halanay inequality and switched systems methodology, a sufficient condition for globally exponential stability of the error system is established. Meanwhile, the upper bound of transmission failure rate is given, which reflects to be closely related to sampling period and the upper bound of node delays. Furthermore, the desired estimator gain of each node is explicitly provided by solving a set of matrix inequalities. Finally, a numerical simulation is carried out to verify the effectiveness of the inferred results.

The topic of delay-dependent extended dissipative analysis for generalized Markovian switching neural networks (GMSNNs) with two delay components is considered in this paper. Based on the concept of the extended dissipativity, this paper is to solve the H ∞ , L 2 − L ∞ , passive and ( Q, S, R )- dissipativity performance in a unified framework. By means of an augmented Lyapunov–Krasovskii functional (LKF) as well as employing the novel free-matrix-based inequality and the reciprocally convex approach, some improved delay-dependent criteria are established in terms of linear matrix inequalities (LMIs). Moreover, the obtained criteria are extended to analyze the extended dissipative analysis of generalized neural networks (GNNs) with two delay components. Numerical examples are shown to illustrate the effectiveness of the methods.

The new dynamic crossover and entropy-based two-combination mutation operations are constructed to prevent the convergence of the algorithms to a local optimum by adaptively modifying the probabilities of crossover and mutation as well as mutation step size according to dynamic adjusting strategies and judging criterions.An improved self-adaptive cellular genetic algorithm (IDCGA) is presented for a more efficient search by combining the Arnold cat map with modified evolution rule, as well as the constructed dynamic crossover and the entropy based two-combination mutation operators.Two novel adaptive fuzzy clustering algorithms based on IDCGA, referred to as IDCGA-FCM and IDCGA2-FCM, are proposed in this paper. The first one is a standalone form for fuzzy clustering on the basis of IDCGA. The second one is a hybrid method based on FCM and IDCGA which takes advantage of the merits of both algorithms.The experimental results showed that the presented algorithms have high efficiency and accuracy. With an aim to overcome low efficiency and improve the performance of fuzzy clustering, two novel fuzzy clustering algorithms based on improved self-adaptive cellular genetic algorithm (IDCGA) are proposed in this paper. The new dynamic crossover and entropy-based two-combination mutation operations are constructed to prevent the convergence of the algorithms to a local optimum by adaptively modifying the probabilities of crossover and mutation as well as mutation step size according to dynamic adjusting strategies and judging criterions. Arnold cat map is employed to initialize population for the purpose of overcoming the sensitivity of the algorithms to initial cluster centers. A modified evolution rule is introduced to build a dynamic environment so as to explore the search space more effectively. Then a new IDCGA that combined these three processes is used to optimize fuzzy c-means (FCM) clustering (IDCGA-FCM). Furthermore, an optimal-selection-based strategy is presented by the golden section method and then a hybrid fuzzy clustering method (IDCGA2-FCM) is developed by automatically integrating IDCGA with optimal-selection-based FCM according to the variation of population entropy. Experiments were performed with six synthetic datasets and seven real-world datasets to compare the performance of our IDCGA-based clustering algorithms with FCM, other GA-based and PSO-based clustering methods. The results showed that the presented algorithms have high efficiency and accuracy.

The complex dynamic networks contains time-varying inner coupling.Event-triggered communication largely decrease the number of information updates.A useful lemma is given to analyze the convergence of the error dynamical system.A sufficient condition is derived to guarantee the exponential synchronization.The Zeno behavior is excluded as well by the strictly positive sampling intervals. This paper investigates the problem of the exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication. The network topology is assumed to have a spanning tree. A sufficient condition is derived to guarantee the exponential synchronization by employing the special Lyapunov stability analysis method, which by combining the difference and differential of the Lyapunov function rather than the single difference or differential. The main advantage of this paper is to avoid continuous communication between network nodes, which can decrease the number of information updates, reduce the network congestion and avoid the waste of network resources. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals. Finally, A simulation example is given to show the effectiveness of the proposed exponential synchronization criteria.

In this paper, the problems of robust stability and standard L1-gain performance analysis of continuous-time positive switched T-S fuzzy systems with interval uncertainties are first investigated. By utilizing a time-scheduled multiple linear copositive Lyapunov function (TSMLCLF) which is time-varying during the mode-dependent minimum dwell time interval, sufficient conditions of asymptotical stability with standard L1-gain performance of the interval positive switched T-S fuzzy systems with mode-dependent dwell time are derived. All the results in the paper are presented in the form of linear programming. Finally, a numerical example is presented to show the effectiveness of the obtained theoretical results.

This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zero-one programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time.

This paper is concerned with the non-fragile H ∞ state estimation problem for a class of discrete-time networked system with probabilistic diverging disturbance and multiple missing measurements. The measurement missing phenomenon is assumed to occur randomly and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 0 , 1 . The aim of this paper is to estimate the networked system by designing a non-fragile H ∞ estimator such that the augmented estimation error system is asymptotically mean square stable with a prescribed H ∞ disturbance attention level γ. By using the Lyapunov method and stochastic analysis, we derive a sufficient condition for the existence of the desired estimator. By solving the linear matrix inequalities (LMIs), the estimator gain matrix is given. Two numerical examples are employed to demonstrate the effectiveness and applicability of the proposed design technique.

In this paper, the consensus of fractional-order multi-agent systems with general linear models is investigated , where the fractional-order α satisfies 0 < α ź n for any given natural number n. A distributed observer-type protocol is proposed. By applying the fractional-order stability theory, properties of the Kronecker product, Mittag-Leffler function and Laplace transform, a sufficient condition is obtained under the assumption that each agent is stabilizable and detectable. Finally, a numerical simulation is presented to illustrate the usefulness of the theoretical result, which shows that the result obtained in this paper generalizes and improves some existing results in literature.

Image set representation and classification is an important problem in computer vision and pattern recognition area. It has been widely used in many computer vision applications. In this paper, a new image set representation and classification method has been proposed. The main contributions of this paper are twofold: (1) a new image set representation model, called attributed covariate-relation graph (ACRG), has been proposed for image set representation and modeling. ACRG aims to represent image set with an attributed graph model which involves both image features and their spatial structure simultaneously. (2) A new graph data based sparse representation and classification method, called Graph Sparse Representation Classification (GSRC) has been proposed to achieve ACRG classification. Experimental results on several datasets demonstrate the benefits of the proposed ACRG representation and GSRC classification. HighlightsA novel attributed covariate-relation graph has been proposed for image set modeling.A new graph sparse representation classification has been proposed for classification.Experimental results show the better performance of method.

This paper investigates issues of finite-time topological identification and stochastic synchronization for two complex networks with multiple time delays. In the paper, we propose two different approaches to identify the topological structure and guarantee stochastic synchronization for complex networks in finite time, which are achieved based on finite-time stability theory and properties of Wiener process. Several useful finite-time synchronization and identification criteria are obtained simultaneously based on adaptive feedback control method. In the final section, numerical examples are examined to illustrate the effectiveness of the analytical results.

This paper concentrates on the extended dissipativity of memristive neural networks with two additive time-varying delays. After giving a foundation to the memristive model, the paper establishes some fundamental results on quadratically stability and extended dissipativity criteria by means of the Lyapunov functional, integral inequality, as well as the relationship between time-varying delays. The novel extended dissipative inequality contains several weighting matrices, by converting the weighting matrices in a new performance index, the extended dissipativity will be degraded to the H ∞ performance, L 2 − L ∞ performance, passivity and dissipativity, respectively. Finally, one example is given to substantiate the significant improvement of the theoretical approaches.

Schatten norm, especially nuclear norm (p=1) has been widely used as an approximation of matrix rank and regularized term in the criterion function in pattern recognition and machine learning. In this paper, we point out that Schatten norm (p1) is also an effective and robust distance metric in the classification stage and can help improve the classification accuracy of matrix based feature extraction methods. Extensive experiments illustrate the effectiveness of Schatten norm (p1). In this paper, we point out that: Schatten norm (p1) is robust to outliers.Schatten norm is also a robust distance metric in the classification stage.Schatten norm helps improve the classification accuracy of feature extraction methods.

In this paper, the impulsive synchronization of fractional order chaotic systems with time-delay is investigated. Based on Lyapunov stability theory and linear matrix inequalities, the impulsive synchronization of same structure and different structure fractional order chaotic systems with time-delay is discussed respectively. Some sufficient conditions for synchronization of the above systems are obtained. Numerical simulation is presented to illustrate the effectiveness of the results obtained in this paper.

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 -group consensus tracking. Especially, for a special graph with acyclic partition, a necessary and sufficient condition of -group consensus tracking is established. Finally, simulation examples are given to illustrate the effectiveness of our results.

In this paper, a fractional-order (and an integer-order) memristor-based system with the flux-controlled memristor characterized by smooth quadratic nonlinearity is proposed and detailed dynamical analysis is carried out by means of theoretical and numerical methods. To be more specific, stability of each equilibrium point in the equilibrium set is analyzed for the integer-order memristive system. Meanwhile, dynamical behavior depending on the initial states of the memristor is investigated and dynamical bifurcation depending on the slope of the memductance function is also considered. The bifurcation analysis is verified by numerical methods, including phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, and Poincare mappings. For the fractional-order case, based on the fractional-order stability theory, stability analysis is carried out just for a certain equilibrium point. Moreover, bifurcation behavior depending on the incommensurate order is discussed by virtue of numerical methods based on the Adams–Bashforth–Moulton algorithm. This paper indicates how the fractional order model and the initial state of the memristor extend the dynamical behaviors of the traditional chaotic systems.