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In multiple instance learning problems, patterns are often given as bags and each bag consists of some instances. Most of existing research in the area focuses on multiple instance classification and multiple instance regression, while very limited work has been conducted for multiple instance clustering (MIC). This paper formulates a novel framework, maximum margin multiple instance clustering (M(3)IC), for MIC. However, it is impractical to directly solve the optimization problem of M(3)IC. Therefore, M(3)IC is relaxed in this paper to enable an efficient optimization solution with a combination of the constrained concave-convex procedure and the cutting plane method. Furthermore, this paper presents some important properties of the proposed method and discusses the relationship between the proposed method and some other related ones. An extensive set of empirical results are shown to demonstrate the advantages of the proposed method against existing research for both effectiveness and efficiency.

In safety critical applications, control architectures based on adaptive neural networks (NNs) must satisfy strict design specifications. This paper presents a practical approach for designing a mixed linear/adaptive model reference controller that recovers the performance of a reference model, and guarantees the boundedness of the tracking error within an a priori specified compact domain, in the presence of bounded uncertainties. The linear part of the controller results from the solution of an optimization problem where specifications are expressed as linear matrix inequality constraints. The linear controller is then augmented with a general adaptive NN that compensates for the uncertainties. The only requirement for the NN is that its output must be confined within pre-specified saturation limits. Toward this end a specific NN output confinement algorithm is proposed in this paper. The main advantages of the proposed approach are that requirements in terms of worst-case performance can be easily defined during the design phase, and that the design of the adaptation mechanism is largely independent from the synthesis of the linear controller. A numerical example is used to illustrate the design methodology.

This paper introduces the Clifford support vector machines (CSVM) as a generalization of the real and complex-valued support vector machines using the Clifford geometric algebra. In this framework, we handle the design of kernels involving the Clifford or geometric product. In this approach, one redefines the optimization variables as multivectors. This allows us to have a multivector as output. Therefore, we can represent multiple classes according to the dimension of the geometric algebra in which we work. We show that one can apply CSVM for classification and regression and also to build a recurrent CSVM. The CSVM is an attractive approach for the multiple input multiple output processing of high-dimensional geometric entities. We carried out comparisons between CSVM and the current approaches to solve multiclass classification and regression. We also study the performance of the recurrent CSVM with experiments involving time series. The authors believe that this paper can be of great use for researchers and practitioners interested in multiclass hypercomplex computing, particularly for applications in complex and quaternion signal and image processing, satellite control, neurocomputation, pattern recognition, computer vision, augmented virtual reality, robotics, and humanoids.

Soft computing (SC) emerged as an integrating framework for a number of techniques that could complement one another quite well (artificial neural networks, fuzzy systems, evolutionary algorithms, probabilistic reasoning). Since its inception, a distinctive goal has been to dig out the deep relationships among their components. This paper considers two wide families of SC models. On the one hand, the regime-switching autoregressive paradigm is a recent development in statistical time series modeling, and it includes a set of models closely related to artificial neural networks. On the other hand, we consider fuzzy rule-based systems in the framework of time series analysis. This paper discloses original results establishing functional equivalences between models of these two classes, and hence opens the door to a productive line of research where results and techniques from one area can be applied in the other. As a consequence of the equivalences presented in this paper, we prove the asymptotic stationarity of a class of fuzzy rule-based systems. Simulations based on information criteria show the importance of the selection of the proper membership function.

This paper is concerned with the problem of exponential stability analysis of continuous-time switched delayed neural networks. By using the average dwell time approach together with the piecewise Lyapunov function technique and by combining a novel Lyapunov-Krasovskii functional, which benefits from the delay partitioning method, with the free-weighting matrix technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time-varying delays, respectively. Moreover, the decay estimates are explicitly given. The results reported in this paper not only depend upon the delay but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.

A crucial issue in designing learning machines is to select the correct model parameters. When the number of available samples is small, theoretical sample-based generalization bounds can prove effective, provided that they are tight and track the validation error correctly. The maximal discrepancy (MD) approach is a very promising technique for model selection for support vector machines (SVM), and estimates a classifier's generalization performance by multiple training cycles on random labeled data. This paper presents a general method to compute the generalization bounds for SVMs, which is based on referring the SVM parameters to an unsupervised solution, and shows that such an approach yields tight bounds and attains effective model selection. When one estimates the generalization error, one uses an unsupervised reference to constrain the complexity of the learning machine, thereby possibly decreasing sharply the number of admissible hypothesis. Although the methodology has a general value, the method described in the paper adopts vector quantization (VQ) as a representation paradigm, and introduces a biased regularization approach in bound computation and learning. Experimental results validate the proposed method on complex real-world data sets.

In the literature, it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns, better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions. This paper, from the viewpoint of the anti-integrable limit, elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions. Particularly, by virtue of the anti-integrable limit technique, this paper shows that any finite-dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model's memory capacity and pattern-retrieval ability. To some extent, this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern-retrieval ability of the artificial neural network models.

This paper presents a subgradient-based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function, a class of affine equality constraints, and a class of nonsmooth convex inequality constraints. The proposed neural network is modeled with a differential inclusion. Under a suitable assumption on the constraint set and a proper assumption on the objective function, it is proved that for a sufficiently large penalty parameter, there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter. It is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network, and coincides with the set which consists of the critical points of the objective function in the feasible region. A condition is given to ensure the convergence to the equilibrium point set in finite time. Moreover, under suitable assumptions, the coincidence between the solution to the differential inclusion and the ldquoslow solutionrdquo of it is also proved. Furthermore, three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network.

The self-organizing network (SON)-based multiple model system is a recently proposed method for identifying the dynamics of a general nonlinear system. It has been observed by researchers that cooperative learning among neighboring regions is sometimes important for the success of identification of a nonlinear system under the multiple model system framework. In this paper, we intend to formally evaluate the effects of cooperative learning and topology preservation in identification of multiple model system based on SON. The results of the mathematical analysis supports the heuristic that a good learning strategy for identifying the local model parameters of a SON-based multiple model system is to choose a neighborhood function whose effective region is initially wider and is reduced gradually during learning. An example of nonlinear function approximation is also provided at the end of this paper to demonstrate the results of the mathematical analysis.

As is well known in statistics, the resulting linear regressors by using the rank-based Wilcoxon approach to linear regression problems are usually robust against (or insensitive to) outliers. This motivates us to introduce in this paper the Wilcoxon approach to the area of machine learning. Specifically, we investigate four new learning machines, namely Wilcoxon neural network (WNN), Wilcoxon generalized radial basis function network (WGRBFN), Wilcoxon fuzzy neural network (WFNN), and kernel-based Wilcoxon regressor (KWR). These provide alternative learning machines when faced with general nonlinear learning problems. Simple weights updating rules based on gradient descent will be derived. Some numerical examples will be provided to compare the robustness against outliers for various learning machines. Simulation results show that the Wilcoxon learning machines proposed in this paper have good robustness against outliers. We firmly believe that the Wilcoxon approach will provide a promising methodology for many machine learning problems.

This paper deals with adaptive tracking for discrete-time multiple-input-multiple-output (MIMO) nonlinear systems in presence of bounded disturbances. In this paper, a high-order neural network (HONN) structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF). This paper also includes the respective stability analysis, on the basis of the Lyapunov approach, for the whole controlled system, including the extended Kalman filter (EKF)-based NN learning algorithm. Applicability of the scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.

This paper is concerned with an enhanced independent component analysis (ICA) and its application to face recognition. Typically, face representations obtained by ICA involve unsupervised learning and high-order statistics. In this paper, we develop an enhancement of the generic ICA by augmenting this method by the Fisher linear discriminant analysis (LDA); hence, its abbreviation, FICA. The FICA is systematically developed and presented along with its underlying architecture. A comparative analysis explores four distance metrics, as well as classification with support vector machines (SVMs). We demonstrate that the FICA approach leads to the formation of well-separated classes in low-dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression. The comprehensive experiments are completed for the facial-recognition technology (FERET) face database; a comparative analysis demonstrates that FICA comes with improved classification rates when compared with some other conventional approaches such as eigenface, fisherface, and the ICA itself.

In this paper, we propose a new neural architecture for classification of visual patterns that is motivated by the two concepts of image pyramids and local receptive fields. The new architecture, called pyramidal neural network (PyraNet), has a hierarchical structure with two types of processing layers: Pyramidal layers and one-dimensional (1-D) layers. In the new network, nonlinear two-dimensional (2-D) neurons are trained to perform both image feature extraction and dimensionality reduction. We present and analyze five training methods for PyraNet [gradient descent (GD), gradient descent with momentum, resilient back-propagation (RPROP), Polak-Ribiere conjugate gradient (CG), and Levenberg-Marquadrt (LM)] and two choices of error functions [mean-square-error (mse) and cross-entropy (CE)]. In this paper, we apply PyraNet to determine gender from a facial image, and compare its performance on the standard facial recognition technology (FERET) database with three classifiers: The convolutional neural network (NN), the k-nearest neighbor (k-NN), and the support vector machine (SVM).

In this paper, we consider a new periodic activation function for the multivalued neuron (MVN). The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN outperforms many other neurons and MVN-based neural networks have shown their high potential, the MVN still has a limited capability of learning highly nonlinear functions. A periodic activation function, which is introduced in this paper, makes it possible to learn nonlinearly separable problems and non-threshold multiple-valued functions using a single multivalued neuron. We call this neuron a multivalued neuron with a periodic activation function (MVN-P). The MVN-Ps functionality is much higher than that of the regular MVN. The MVN-P is more efficient in solving various classification problems. A learning algorithm based on the error-correction rule for the MVN-P is also presented. It is shown that a single MVN-P can easily learn and solve those benchmark classification problems that were considered unsolvable using a single neuron. It is also shown that a universal binary neuron, which can learn nonlinearly separable Boolean functions, and a regular MVN are particular cases of the MVN-P.

Recurrent neural networks for solving constrained least absolute deviation (LAD) problems or L(1)-norm optimization problems have attracted much interest in recent years. But so far most neural networks can only deal with some special linear constraints efficiently. In this paper, two neural networks are proposed for solving LAD problems with various linear constraints including equality, two-sided inequality and bound constraints. When tailored to solve some special cases of LAD problems in which not all types of constraints are present, the two networks can yield simpler architectures than most existing ones in the literature. In particular, for solving problems with both equality and one-sided inequality constraints, another network is invented. All of the networks proposed in this paper are rigorously shown to be capable of solving the corresponding problems. The different networks designed for solving the same types of problems possess the same structural complexity, which is due to the fact these architectures share the same computing blocks and only differ in connections between some blocks. By this means, some flexibility for circuits realization is provided. Numerical simulations are carried out to illustrate the theoretical results and compare the convergence rates of the networks.

The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.

An unsupervised competitive neural network for efficient clustering of Gaussian probability density function (GPDF) data of continuous density hidden Markov models (CDHMMs) is proposed in this paper. The proposed unsupervised competitive neural network, called the divergence-based centroid neural network (DCNN), employs the divergence measure as its distance measure and utilizes the statistical characteristics of observation densities in the HMM for speech recognition problems. While the conventional clustering algorithms used for the vector quantization (VQ) codebook design utilize only the mean values of the observation densities in the HMM, the proposed DCNN utilizes both the mean and the covariance values. When compared with other conventional unsupervised neural networks, the DCNN successfully allocates more code vectors to the regions where GPDF data are densely distributed while it allocates fewer code vectors to the regions where GPDF data are sparsely distributed. When applied to Korean monophone recognition problems as a tool to reduce the size of the codebook, the DCNN reduced the number of GPDFs used for code vectors by 65.3% while preserving recognition accuracy. Experimental results with a divergence-based k-means algorithm and a divergence-based self-organizing map algorithm are also presented in this paper for a performance comparison.

In this paper, we consider delayed bidirectional associative memory (BAM) neural networks (NNs) with Lipschitz continuous activation functions. By applying Young's inequality and Hoelder's inequality techniques together with the properties of monotonic continuous functions, global exponential stability criteria are established for BAM NNs with time delays. This is done through the use of a new Lyapunov functional and an M-matrix. The results obtained in this paper extend and improve previous results.

A novel radial basis function neural network for discriminant analysis is presented in this paper. In contrast to many other researches, this work focuses on the exploitation of the weight structure of radial basis function neural networks using the Bayesian method. It is expected that the performance of a radial basis function neural network with a well-explored weight structure can be improved. As the weight structure of a radial basis function neural network is commonly unknown, the Bayesian method is, therefore, used in this paper to study this a priori structure. Two weight structures are investigated in this study, i.e., a single-Gaussian structure and a two-Gaussian structure. An expectation-maximization learning algorithm is used to estimate the weights. The simulation results showed that the proposed radial basis function neural network with a weight structure of two Gaussians outperformed the other algorithms.

The convergence of Oja's principal component analysis (PCA) learning algorithms is a difficult topic for direct study and analysis. Traditionally, the convergence of these algorithms is indirectly analyzed via certain deterministic continuous time (DCT) systems. Such a method will require the learning rate to converge to zero, which is not a reasonable requirement to impose in many practical applications. Recently, deterministic discrete time (DDT) systems have been proposed instead to indirectly interpret the dynamics of the learning algorithms. Unlike DCT systems, DDT systems allow learning rates to be constant (which can be a nonzero). This paper will provide some important results relating to the convergence of a DDT system of Oja's PCA learning algorithm. It has the following contributions: 1) A number of invariant sets are obtained, based on which we can show that any trajectory starting from a point in the invariant set will remain in the set forever. Thus, the nondivergence of the trajectories is guaranteed. 2) The convergence of the DDT system is analyzed rigorously. It is proven, in the paper, that almost all trajectories of the system starting from points in an invariant set will converge exponentially to the unit eigenvector associated with the largest eigenvalue of the correlation matrix. In addition, exponential convergence rate are obtained, providing useful guidelines for the selection of fast convergence learning rate. 3) Since the trajectories may diverge, the careful choice of initial vectors is an important issue. This paper suggests to use the domain of unit hyper sphere as initial vectors to guarantee convergence. 4) Simulation results will be furnished to illustrate the theoretical results achieved.

In this letter, we point out that the linear matrix inequality (LMI)-based criterion obtained in the above paper (Singh, IEEE Trans. Neural Netw., vol. 15, no. 1, p. 223-5, 2004) for the global exponential stability of the delayed neural networks can be simplified to a simpler but equivalent form and, thus, show that it is not necessary to have such complex form of condition in the above paper. As a result, we also answer the question raised by the author of the above paper.

This paper is concerned with the passivity and stability problems of reaction-diffusion neural networks (RDNNs) in which the input and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, some sufficient conditions ensuring the passivity and global exponential stability are derived. Furthermore, when the parameter uncertainties appear in RDNNs, several criteria for robust passivity and robust global exponential stability are also presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

In this paper, a one-layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints. The global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex. The finite-time state convergence to the feasible region defined by the equality constraints is also proved. In addition, global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region. Simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network.

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman equation forward-in-time for the decentralized near optimal regulation of a class of nonlinear interconnected discrete-time systems with unknown internal subsystem and interconnection dynamics, while the input gain matrix is considered known. Even though the unknown interconnection terms are considered weak and functions of the entire state vector, the decentralized control is attempted under the assumption that only the local state vector is measurable. The decentralized nearly optimal controller design for each subsystem consists of two neural networks (NNs), an action NN that is aimed to provide a nearly optimal control signal, and a critic NN which evaluates the performance of the overall system. All NN parameters are tuned online for both the NNs. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded and that the synthesized subsystems inputs approach their corresponding nearly optimal control inputs with bounded error. Simulation results are included to show the effectiveness of the approach.

In this paper, we have three goals: the first is to delineate the advantages of a variably delayed system, the second is to find a more intuitive Lyapunov function for a delayed neural network, and the third is to design a delayed neural network for a quadratic cost function. For delayed neural networks, most researchers construct a Lyapunov function based on the linear matrix inequality (LMI) approach. However, that approach is not intuitive. We provide a alternative candidate Lyapunov function for a delayed neural network. On the other hand, if we are first given a quadratic cost function, we can construct a delayed neural network by suitably dividing the second-order term into two parts: a self-feedback connection weight and a delayed connection weight. To demonstrate the advantage of a variably delayed neural network, we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than Chen-Aihara's model, Wang's model, and Zhao's model. We discuss both the chaotic and the convergent phases. During the chaotic phase, we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay. We show that the variably delayed model possesses the stochastic property and chaotic wandering. During the convergent phase, we not only provide a novel Lyapunov function for neural networks with a delay (the Lyapunov function is independent of the LMI approach) but also establish a correlation between the Lyapunov function for a delayed neural network and an objective function for the traveling salesman problem.

This paper investigates a neural network (NN) state observer-based adaptive control for a class of time-varying delays nonlinear systems with unknown control direction. An adaptive neural memoryless observer, in which the knowledge of time-delay is not used, is designed to estimate the system states. Furthermore, by applying the property of the function tanh(2)(ϑ/ε)/ϑ (the function can be defined at ϑ = 0) and introducing a novel type appropriate Lyapunov-Krasovskii functional, an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time-delay. It is highly proven that the closed-loop systems controller designed by the NN-basis function property, new kind parameter adaptive law and Nussbaum function in detecting the control direction is able to guarantee the semi-global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero. The characteristic of the proposed approach is that it relaxes any restrictive assumptions of Lipschitz condition for the unknown nonlinear continuous functions. And the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states. Finally, two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach.

In this paper, a class of impulsive interval neural networks with discrete and distributed time-varying delays is discussed. Several new sufficient conditions are obtained ensuring the existence, uniqueness, and global exponential stability of periodic solution (i.e., stationary oscillation) for the addressed models based on inequality analysis techniques. The obtained results can be checked easily by the linear matrix inequality control toolbox in MATLAB. Finally, two numerical examples are given to show the effectiveness of our results.

Smooth hinging hyperplane (SHH) has been proposed as an improvement over the well-known hinging hyperplane (HH) by the fact that it retains the useful features of HH while overcoming HH's drawback of nondifferentiability. This paper introduces a formal characterization of smooth hinge function (SHF), which can be used to generate SHH as a neural network. A method for the general construction of SHF is also given. Furthermore, the work proves that SHH is better than HH in functional approximation, i.e., the optimal error of SHH approximating a general function is always smaller or equal to that of HH. Particularly, in the case that the SHF is generated via the integration of a class of sigmoidal functions, it is further proven that the corresponding SHH of the 2m SHFs would outperform a neural network with m of the sigmoidal function from which the SHF is derived. Any upper bound established on the approximation error of a neural network of m sigmoidal activation functions can hence be translated to the SHH of m SHFs by replacing m with [m/2]. The work also includes an algorithm for the identification of SHH making use of its differentiability property. Simulation experiments are presented to validate the theoretical conclusions to possible extent.

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

This paper discusses the problem of what kind of learning model is suitable for the tasks of feature extraction for data representation and suggests two evaluation criteria for nonlinear feature extractors: reconstruction error minimization and similarity preservation. Based on the suggested evaluation criteria, a new type of principal curve-similarity preserving principal curve (SPPC) is proposed. SPPCs minimize the reconstruction error under the condition that the similarity between similar samples are preserved in the extracted features, thus giving researchers effective and reliable cognition of the inner structure of data sets. The existence and properties of SPPCs are analyzed; a practical learning algorithm is proposed and high dimensional extensions of SPPCs are also discussed. Experimental results show the virtues of SPPCs in preserving inner structures of data sets and discovering manifolds with high nonlinearity.

We study finite-state, finite-action, discounted infinite-horizon Markov decision processes with uncertain correlated transition matrices in deterministic policy spaces. Existing robust dynamic programming methods cannot be extended to solving this class of general problems. In this paper, based on a robust optimality criterion, an approximate robust policy iteration using a multilayer perceptron neural network is proposed. It is proven that the proposed algorithm converges in finite iterations, and it converges to a stationary optimal or near-optimal policy in a probability sense. In addition, we point out that sometimes even a direct enumeration may not be applicable to addressing this class of problems. However, a direct enumeration based on our proposed maximum value approximation over the parameter space is a feasible approach. We provide further analysis to show that our proposed algorithm is more efficient than such an enumeration method for various scenarios.

The weight-decay technique is an effective approach to handle overfitting and weight fault. For fault-free networks, without an appropriate value of decay parameter, the trained network is either overfitted or underfitted. However, many existing results on the selection of decay parameter focus on fault-free networks only. It is well known that the weight-decay method can also suppress the effect of weight fault. For the faulty case, using a test set to select the decay parameter is not practice because there are huge number of possible faulty networks for a trained network. This paper develops two mean prediction error (MPE) formulae for predicting the performance of faulty radial basis function (RBF) networks. Two fault models, multiplicative weight noise and open weight fault, are considered. Our MPE formulae involve the training error and trained weights only. Besides, in our method, we do not need to generate a huge number of faulty networks to measure the test error for the fault situation. The MPE formulae allow us to select appropriate values of decay parameter for faulty networks. Our experiments showed that, although there are small differences between the true test errors (from the test set) and the MPE values, the MPE formulae can accurately locate the appropriate value of the decay parameter for minimizing the true test error of faulty networks.

Recently, the minimum error entropy (MEE) criterion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance surface even for adaptive linear neuron (ADALINE) training, which complicates the theoretical analysis of the method. In this paper, we develop a unified approach for mean-square convergence analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square convergence analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.

In this paper, based on a one-neuron recurrent neural network, a novel k-winners-take-all (k -WTA) network is proposed. Finite time convergence of the proposed neural network is proved using the Lyapunov method. The k-WTA operation is first converted equivalently into a linear programming problem. Then, a one-neuron recurrent neural network is proposed to get the kth or (k + 1)th largest inputs of the k-WTA problem. Furthermore, a k-WTA network is designed based on the proposed neural network to perform the k-WTA operation. Compared with the existing k-WTA networks, the proposed network has simple structure and finite time convergence. In addition, simulation results on numerical examples show the effectiveness and performance of the proposed k-WTA network.

This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.

The Adachi neural network (AdNN) is a fascinating neural network (NN) which has been shown to possess chaotic properties, and to also demonstrate associative memory (AM) and pattern recognition (PR) characteristics. Variants of the AdNN have also been used to obtain other PR phenomena, and even blurring. An unsurmountable problem associated with the AdNN and the variants referred to above is that all of them require a quadratic number of computations. This is essentially because the NNs in each case are completely connected graphs. In this paper, we consider how the computations can be significantly reduced by merely using a linear number of computations. To achieves this, we extract from the original completely connected graph one of its spanning trees. We then address the problem of computing the weights for this spanning tree. This is done in such a manner that the modified tree-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new linear-time AdNN-like network possesses chaotic and PR properties for different settings. As far as we know, such a tree-based AdNN has not been reported, and the results given here are novel.

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained.

In this paper, a delayed projection neural network is proposed for solving a class of linear variational inequality problems. The theoretical analysis shows that the proposed neural network is globally exponentially stable under different conditions. By the proposed linear matrix inequality (LMI) method, the monotonicity assumption on the linear variational inequality is no longer necessary. By employing Lagrange multipliers, the proposed method can resolve the constrained quadratic programming problems. Finally, simulation examples are given to demonstrate the satisfactory performance of the proposed neural network.

This paper presents a novel recurrent neural network for solving a class of convex quadratic programming (QP) problems, in which the quadratic term in the objective function is the square of the Euclidean norm of the variable. This special structure leads to a set of simple optimality conditions for the problem, based on which the neural network model is formulated. Compared with existing neural networks for general convex QP, the new model is simpler in structure and easier to implement. The new model can be regarded as an improved version of the dual neural network in the literature. Based on the new model, a simple neural network capable of solving the $k$ -winners-take-all ( $k$ -WTA) problem is formulated. The stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results.

In this paper, robust stability problems for interval Cohen-Grossberg neural networks with unknown time-varying delays are investigated. Using linear matrix inequality, M -matrix theory, and Halanay inequality techniques, new sufficient conditions independent of time-varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval Cohen-Grossberg neural networks with time-varying delays. All these results have no restriction on the rate of change of the time-varying delays. Compared to some existing results, these new criteria are less conservative and are more convenient to check. Two numerical examples are used to show the effectiveness of the present results.

An adaptive Fourier neural network (AFNN) control scheme is presented in this paper for the control of a class of uncertain nonlinear systems. Based on Fourier analysis and neural network (NN) theory, AFNN employs orthogonal complex Fourier exponentials as the activation functions. Due to the clear physical meaning of the neurons, the determination of the AFNN structure as well as the parameters of the activation functions becomes convenient. One salient feature of the proposed AFNN approach is that all the nonlinearities and uncertainties of the dynamical system are lumped together and compensated online by AFNN. It can, therefore, be applied to uncertain nonlinear systems without any a priori knowledge about the system dynamics. Derived from Lyapunov theory, a novel learning algorithm is proposed, which is essentially a frequency domain method and can guarantee asymptotic stability of the closed-loop system. The simulation results of a multiple-input-multiple-output (MIMO) nonlinear system and the experimental results of an X - Y positioning table are presented to show the effectiveness of the proposed AFNN controller.

This paper studies the problem of stability analysis for neural networks (NNs) with a time-varying delay. Unlike the previous works, the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Meanwhile, the computational complexity of the newly obtained stability conditions is reduced because less variables are involved. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.

In this paper, we present a neural classifier algorithm that locally approximates the decision surface of labeled data by a patchwork of separating hyperplanes, which are arranged under certain topological constraints similar to those of self-organizing maps (SOMs). We take advantage of the fact that these boundaries can often be represented by linear ones connected by a low-dimensional nonlinear manifold, thus influencing the placement of the separators. The resulting classifier allows for a voting scheme that averages over the classification results of neighboring hyper- planes. Our algorithm is computationally efficient both in terms of training and classification. Further, we present a model selection method to estimate the topology of the classification boundary. We demonstrate the algorithm's usefulness on several artificial and real-world data sets and compare it to the state-of-the-art supervised learning algorithms.

The adaptive-subspace self-organizing map (ASSOM) is useful for invariant feature generation and visualization. However, the learning procedure of the ASSOM is slow. In this paper, two fast implementations of the ASSOM are proposed to boost ASSOM learning based on insightful discussions of the basis rotation operator of ASSOM. We investigate the objective function approximately maximized by the classical rotation operator. We then explore a sequence of two schemes to apply the proposed ASSOM implementations to saliency-based invariant feature construction for image classification. In the first scheme, a cumulative activity map computed from a single ASSOM is used as descriptor of the input image. In the second scheme, we use one ASSOM for each image category and a joint cumulative activity map is calculated as the descriptor. Both schemes are evaluated on a subset of the Corel photo database with ten classes. The multi-ASSOM scheme is favored. It is also applied to adult image filtering and shows promising results.

This paper considers the design of robust neural network tracking controllers for nonlinear systems. The neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to establish a robust neural control system, with guaranteed boundedness for both the input/output (I/O) signals and the weights of the neural network. The neural network is trained by the simultaneous perturbation stochastic approximation (SPSA) method instead of the standard backpropagation (BP) algorithm. The proposed neural control system guarantees closed-loop stability of the estimation system, and a good tracking performance. The performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts, fast convergence, and robustness against system disturbance.

In this paper, we propose a powerful symmetric radial basis function (RBF) classifier for nonlinear detection in the so-called "overloaded" multiple-antenna-aided communication systems. By exploiting the inherent symmetry property of the optimal Bayesian detector, the proposed symmetric RBF classifier is capable of approaching the optimal classification performance using noisy training data. The classifier construction process is robust to the choice of the RBF width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio (SNR) gain in excess of 8 dB against the powerful linear minimum bit error rate (BER) benchmark, when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements.

In this paper, we propose a novel large margin classifier, called the maxi-min margin machine M(4). This model learns the decision boundary both locally and globally. In comparison, other large margin classifiers construct separating hyperplanes only either locally or globally. For example, a state-of-the-art large margin classifier, the support vector machine (SVM), considers data only locally, while another significant model, the minimax probability machine (MPM), focuses on building the decision hyperplane exclusively based on the global information. As a major contribution, we show that SVM yields the same solution as M(4) when data satisfy certain conditions, and MPM can be regarded as a relaxation model of M(4). Moreover, based on our proposed local and global view of data, another popular model, the linear discriminant analysis, can easily be interpreted and extended as well. We describe the M(4) model definition, provide a geometrical interpretation, present theoretical justifications, and propose a practical sequential conic programming method to solve the optimization problem. We also show how to exploit Mercer kernels to extend M(4) for nonlinear classifications. Furthermore, we perform a series of evaluations on both synthetic data sets and real-world benchmark data sets. Comparison with SVM and MPM demonstrates the advantages of our new model.