Search

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, a new kernel-based method for data visualization and dimensionality reduction is proposed. A reference point is considered corresponding to additional constraints taken in the problem formulation. In contrast with the class of kernel eigenmap methods, the solution (coordinates in the low-dimensional space) is characterized by a linear system instead of an eigenvalue problem. The kernel maps with a reference point are generated from a least squares support vector machine (LS-SVM) core part that is extended with an additional regularization term for preserving local mutual distances together with reference point constraints. The kernel maps possess primal and dual model representations and provide out-of-sample extensions, e.g., for validation-based tuning. The method is illustrated on toy problems and real-life data sets.

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.

Hard-margin support vector machines (HM-SVMs) suffer from getting overfitting in the presence of noise. Soft-margin SVMs deal with this problem by introducing a regularization term and obtain a state-of-the-art performance. However, this disposal leads to a relatively high computational cost. In this paper, an alternative method, greedy stagewise algorithm for SVMs, named GS-SVMs, is presented to cope with the overfitting of HM-SVMs without employing the regularization term. The most attractive property of GS-SVMs is that its computational complexity in the worst case only scales quadratically with the size of training samples. Experiments on the large data sets with up to 400,000 training samples demonstrate that GS-SVMs can be faster than LIBSVM 2.83 without sacrificing the accuracy. Finally, we employ statistical learning theory to analyze the empirical results, which shows that the success of GS-SVMs lies in that its early stopping rule can act as an implicit regularization term.

The FastICA algorithm is one of the most prominent methods to solve the problem of linear independent component analysis (ICA). Although there have been several attempts to prove local convergence properties of FastICA, rigorous analysis is still missing in the community. The major difficulty of analysis is because of the well-known sign-flipping phenomenon of FastICA, which causes the discontinuity of the corresponding FastICA map on the unit sphere. In this paper, by using the concept of principal fiber bundles, FastICA is proven to be locally quadratically convergent to a correct separation. Higher order local convergence properties of FastICA are also investigated in the framework of a scalar shift strategy. Moreover, as a parallelized version of FastICA, the so-called QR FastICA algorithm, which employs the QR decomposition (Gram-Schmidt orthonormalization process) instead of the polar decomposition, is shown to share similar local convergence properties with the original FastICA.

Plenty of methods have been proposed in order to discover latent variables (features) in data sets. Such approaches include the principal component analysis (PCA), independent component analysis (ICA), factor analysis (FA), etc., to mention only a few. A recently investigated approach to decompose a data set with a given dimensionality into a lower dimensional space is the so-called nonnegative matrix factorization (NMF). Its only requirement is that both decomposition factors are nonnegative. To approximate the original data, the minimization of the NMF objective function is performed in the Euclidean space, where the difference between the original data and the factors can be minimized by employing L(2)-norm. In this paper, we propose a generalization of the NMF algorithm by translating the objective function into a Hilbert space (also called feature space) under nonnegativity constraints. With the help of kernel functions, we developed an approach that allows high-order dependencies between the basis images while keeping the nonnegativity constraints on both basis images and coefficients. Two practical applications, namely, facial expression and face recognition, show the potential of the proposed approach.

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, stability and bifurcation of a general recurrent neural network with multiple time delays is considered, where all the variables of the network can be regarded as bifurcation parameters. It is found that Hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied. By analyzing the characteristic equation and using the frequency domain method, the existence of Hopf bifurcation is proved. The stability of bifurcating periodic solutions is determined by the harmonic balance approach, Nyquist criterion, and graphic Hopf bifurcation theorem. Moreover, a critical condition is derived under which the stability is not guaranteed, thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood, and from which the essential dynamics of the delayed neural network are revealed. Finally, numerical results are given to verify the theoretical analysis, and some interesting phenomena are observed and reported.

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

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 use complex analytic functions to achieve independent component analysis (ICA) by maximization of non-Gaussianity and introduce the complex maximization of non-Gaussianity (CMN) algorithm. We derive both a gradient-descent and a quasi-Newton algorithm that use the full second-order statistics providing superior performance with circular and noncircular sources as compared to existing methods. We show the connection among ICA methods through maximization of non-Gaussianity, mutual information, and maximum likelihood (ML) for the complex case, and emphasize the importance of density matching for all three cases. Local stability conditions are derived for the CMN cost function that explicitly show the effects of noncircularity on convergence and demonstrated through simulation examples.

Blind inversion of a linear and instantaneous mixture of source signals is a problem often encountered in many signal processing applications. Efficient fastICA (EFICA) offers an asymptotically optimal solution to this problem when all of the sources obey a generalized Gaussian distribution, at most one of them is Gaussian, and each is independent and identically distributed (i.i.d.) in time. Likewise, weights-adjusted second-order blind identification (WASOBI) is asymptotically optimal when all the sources are Gaussian and can be modeled as autoregressive (AR) processes with distinct spectra. Nevertheless, real-life mixtures are likely to contain both Gaussian AR and non-Gaussian i.i.d. sources, rendering WASOBI and EFICA severely suboptimal. In this paper, we propose a novel scheme for combining the strengths of EFICA and WASOBI in order to deal with such hybrid mixtures. Simulations show that our approach outperforms competing algorithms designed for separating similar mixtures.

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.

It is well known that least absolute deviation (LAD) criterion or L(1)-norm used for estimation of parameters is characterized by robustness, i.e., the estimated parameters are totally resistant (insensitive) to large changes in the sampled data. This is an extremely useful feature, especially, when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise. In our previous works, we have proposed the least absolute deviation neural network (LADNN) to solve unconstrained LAD problems. The theoretical proofs and numerical simulations have shown that the LADNN is Lyapunov-stable and it can globally converge to the exact solution to a given unconstrained LAD problem. We have also demonstrated its excellent application value in time-delay estimation. More generally, a practical LAD application problem may contain some linear constraints, such as a set of equalities and/or inequalities, which is called constrained LAD problem, whereas the unconstrained LAD can be considered as a special form of the constrained LAD. In this paper, we present a new neural network called constrained least absolute deviation neural network (CLADNN) to solve general constrained LAD problems. Theoretical proofs and numerical simulations demonstrate that the proposed CLADNN is Lyapunov stable and globally converges to the exact solution to a given constrained LAD problem, independent of initial values. The numerical simulations have also illustrated that the proposed CLADNN can be used to robustly estimate parameters for nonlinear curve fitting, which is extensively used in signal and image processing.

This paper studies the problems of global exponential stability for impulsive high-order Hopfield-type neural networks (NNs) with time-varying delays. By employing the Lyapunov-Razumikhin technique, some criteria ensuring global exponential stability are derived. Our results are then used to obtain some sufficient conditions under which some NNs can be forced to converge by impulsive control. Numerical examples are also discussed to illustrate our results.

In this paper, a neuroadaptive control framework for continuous- and discrete-time nonlinear uncertain dynamical systems with input-to-state stable internal dynamics is developed. The proposed framework is Lyapunov based and unlike standard neural network (NN) controllers guaranteeing ultimate boundedness, the framework guarantees partial asymptotic stability of the closed-loop system, that is, asymptotic stability with respect to part of the closed-loop system states associated with the system plant states. The neuroadaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuously differentiable and that the approximation error of uncertain system nonlinearities lie in a small gain-type norm bounded conic sector. This allows us to merge robust control synthesis tools with NN adaptive control tools to guarantee system stability. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

In this paper, we modify the fuzzy ARTMAP (FA) neural network (NN) using the Bayesian framework in order to improve its classification accuracy while simultaneously reduce its category proliferation. The proposed algorithm, called Bayesian ARTMAP (BA), preserves the FA advantages and also enhances its performance by the following: (1) representing a category using a multidimensional Gaussian distribution, (2) allowing a category to grow or shrink, (3) limiting a category hypervolume, (4) using Bayes' decision theory for learning and inference, and (5) employing the probabilistic association between every category and a class in order to predict the class. In addition, the BA estimates the class posterior probability and thereby enables the introduction of loss and classification according to the minimum expected loss. Based on these characteristics and using synthetic and 20 real-world databases, we show that the BA outperformes the FA, either trained for one epoch or until completion, with respect to classification accuracy, sensitivity to statistical overlapping, learning curves, expected loss, and category proliferation.

This paper is concerned with the problem of local and global asymptotic stability for a class of discrete-time recurrent neural networks, which provide discrete-time analogs to their continuous-time counterparts, i.e., continuous-time recurrent neural networks with distributed delay. Some stability criteria, which include some existing results as their special cases, are derived. A discussion about the dynamical consistence of discrete-time neural networks versus their continuous-time counterparts is provided. An unconventional finite difference method is proposed and an example is also given to show the effectiveness of the method.

Independent component analysis (ICA) is currently the most popularly used approach to blind source separation (BSS), the problem of recovering unknown source signals when their mixtures are observed but the actual mixing process is unknown. Many ICA algorithms assume that a fixed set of source signals consistently exists in mixtures throughout the time-series to be examined. However, real-world signals often have such difficult nonstationarity that each source signal abruptly appears or disappears, thus the set of active sources dynamically changes with time. In this paper, we propose switching ICA (SwICA), which focuses on such situations. The proposed approach is based on the noisy ICA formulated as a generative model. We employ a special type of hidden Markov model (HMM) to represent such prior knowledge that the source may abruptly appear or disappear with time. The special HMM setting t hen provides an effect ofvariable selection in a dynamic way. We use the variational Bayes (VB) method to derive an effective approximation of Bayesian inference for this model. In simulation experiments using artificial and realistic source signals, the proposed method exhibited performance superior to existing methods, especially in the presence of noise. The compared methods include the natural-gradient ICA with a nonholonomic constraint, and the existing ICA method incorporating an HMM source model, which aims to deal with general nonstationarities that may exist in source signals. In addition, the proposed method could successfully recover the source signals even when the total number of true sources was overestimated or was larger than that of mixtures. We also propose a modification of the basic Markov model into a semi-Markov model, and show that the semi-Markov one is more effective for robust estimation of the source appearance.

International audience; Mapping high-dimensional data in a low-dimensional space, for example, for visualization, is a problem of increasingly major concern in data analysis. This paper presents data-driven high-dimensional scaling (DD-HDS), a nonlinear mapping method that follows the line of multidimensional scaling (MDS) approach, based on the preservation of distances between pairs of data. It improves the performance of existing competitors with respect to the representation of high-dimensional data, in two ways. It introduces (1) a specific weighting of distances between data taking into account the concentration of measure phenomenon and (2) a symmetric handling of short distances in the original and output spaces, avoiding false neighbor representations while still allowing some necessary tears in the original distribution. More precisely, the weighting is set according to the effective distribution of distances in the data set, with the exception of a single user-defined parameter setting the tradeoff between local neighborhood preservation and global mapping. The optimization of the stress criterion designed for the mapping is realized by "force-directed placement" (FDP). The mappings of low- and high-dimensional data sets are presented as illustrations of the features and advantages of the proposed algorithm. The weighting function specific to high-dimensional data and the symmetric handling of short distances can be easily incorporated in most distance preservation-based nonlinear dimensionality reduction methods.

This paper proposes polytope ARTMAP (PTAM), an adaptive resonance theory (ART) network for classification tasks which does not use the vigilance parameter. This feature is due to the geometry of categories in PTAM, which are irregular polytopes whose borders approximate the borders among the output predictions. During training, the categories expand only towards the input pattern without category overlap. The category expansion in PTAM is naturally limited by the other categories, and not by the category size, so the vigilance is not necessary. PTAM works in a fully automatic way for pattern classification tasks, without any parameter tuning, so it is easier to employ for nonexpert users than other classifiers. PTAM achieves lower error than the leading ART networks on a complete collection of benchmark data sets, except for noisy data, without any parameter optimization.

A Bayesian Gaussian process (GP) modeling approach has recently been introduced to model-based control strategies. The estimate of the variance of the predicted output is the most useful advantage of GPs in comparison to neural networks (NNs) and fuzzy models. However, the GP model is computationally demanding and nontransparent. To reduce the computation load and increase transparency, a local linear GP model network is proposed in this paper. The proposed methodology combines the local model network principle with the GP prior approach. A novel algorithm for structure determination and optimization is introduced, which is widely applicable to the training of local model networks. The modeling procedure of the local linear GP (LGP) model network is demonstrated on an example of a nonlinear laboratory scale process rig.

In order to conveniently analyze the stability of recurrent neural networks (RNNs) and successfully synthesize the controllers for nonlinear systems, similar to the nominal model in linear robust control theory, the novel neural network model, named delayed standard neural network model (DSNNM) is presented, which is the interconnection of a linear dynamic system and a bounded static delayed (or nondelayed) nonlinear operator. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability for the continuous-time DSNNMs (CDSNNMs) and discrete-time DSNNMs (DDSNNMs) are derived, whose conditions are formulated as linear matrix inequalities (LMIs). Based on the stability analysis, some state-feedback control laws for the DSNNM with input and output are designed to stabilize the closed-loop systems. Most RNNs and neurocontrol nonlinear systems with (or without) time delays can be transformed into the DSNNMs to be stability-analyzed or stabilization-synthesized in a unified way. In this paper, the DSNNMs are applied to analyzing the stability of the continuous-time and discrete-time RNNs with or without time delays, and synthesizing the state-feedback controllers for the chaotic neural-network-system and discrete-time nonlinear system. It turns out that the DSNNM makes the stability conditions of the RNNs easily verified, and provides a new idea for the synthesis of the controllers for the nonlinear systems.

In this paper, we present a novel scheme for linear feature extraction in classification. The method is based on the maximization of the mutual information (MI) between the features extracted and the classes. The sum of the MI corresponding to each of the features is taken as an heuristic that approximates the MI of the whole output vector. Then, a component-by-component gradient-ascent method is proposed for the maximization of the MI, similar to the gradient-based entropy optimization used in independent component analysis (ICA). The simulation results show that not only is the method competitive when compared to existing supervised feature extraction methods in all cases studied, but it also remarkably outperform them when the data are characterized by strongly nonlinear boundaries between classes.

In this paper, we present an empirical study of iterative least squares minimization of the Hamilton-Jacobi-Bellman (HJB) residual with a neural network (NN) approximation of the value function. Although the nonlinearities in the optimal control problem and NN approximator preclude theoretical guarantees and raise concerns of numerical instabilities, we present two simple methods for promoting convergence, the effectiveness of which is presented in a series of experiments. The first method involves the gradual increase of the horizon time scale, with a corresponding gradual increase in value function complexity. The second method involves the assumption of stochastic dynamics which introduces a regularizing second derivative term to the HJB equation. A gradual reduction of this term provides further stabilization of the convergence. We demonstrate the solution of several problems, including the 4-D inverted-pendulum system with bounded control. Our approach requires no initial stabilizing policy or any restrictive assumptions on the plant or cost function, only knowledge of the plant dynamics. In the Appendix, we provide the equations for first- and second-order differential backpropagation.

This paper proposes a self-organizing adaptive fuzzy neural control (SAFNC) via sliding-mode approach for a class of nonlinear systems. The proposed SAFNC system is comprised of a computation controller and a supervisory controller. The computation controller including a self-organizing fuzzy neural network (SOFNN) identifier is the principal controller. The SOFNN identifier is used to online estimate the controlled system dynamics with the structure and parameter learning phases of fuzzy neural network (FNN), simultaneously. The structure learning phase possesses the ability of online generation and elimination of fuzzy rules to achieve optimal neural structure, and the parameter learning phase adjusts the interconnection weights of neural network to achieve favorable approximation performance. The supervisory controller is used to achieve the L2-norm bound tracking performance with a desired attenuation level. Moreover, all the parameter learning algorithms are derived based on Lyapunov function candidate, thus the system stability can be guaranteed. Finally, simulation results show that the SAFNC can achieve favorable tracking performances.

A neural control synthesis method is considered for a class of nonaffine uncertain single-input-single-output (SISO) systems. The method eliminates a fixed-point assumption and does not assume boundedness on the time derivative of a control effectiveness term. One or the other of these assumptions exist in earlier papers on this subject. Using Lyapunov's direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded, and that the tracking error converges to an adjustable neighborhood of the origin. Simulation with a Van Der Pol equation with nonaffine control terms illustrates the approach.

In this paper, we present two fast sparse approximation schemes for least squares support vector machine (LS-SVM), named FSALS-SVM and PFSALS-SVM, to overcome the limitation of LS-SVM that it is not applicable to large data sets and to improve test speed. FSALS-SVM iteratively builds the decision function by adding one basis function from a kernel-based dictionary at one time. The process is terminated by using a flexible and stable epsilon insensitive stopping criterion. A probabilistic speedup scheme is employed to further improve the speed of FSALS-SVM and the resulting classifier is named PFSALS-SVM. Our algorithms are of two compelling features: low complexity and sparse solution. Experiments on benchmark data sets show that our algorithms obtain sparse classifiers at a rather low cost without sacrificing the generalization performance.

In this paper, a novel exemplar-based constructive approach using kernels is proposed for simultaneous pattern classification and multidomain pattern association tasks. The kernel networks are constructed on a modular basis by a simple one-shot self-structuring algorithm motivated from the traditional Hebbian principle and then, they act as the flexible memory capable of generalization for the respective classes. In the self-structuring kernel memory (SSKM), any arduous and iterative network parameter tuning is not involved for establishing the weight connections during the construction, unlike conventional approaches, and thereby, it is considered that the networks do not inherently suffer from the associated numerical instability. Then, the approach is extended for multidomain pattern association, in which a particular domain input cannot only activate some kernel units (KUs) but also the kernels in other domain(s) via the cross-domain connection(s) in between. Thereby, the SSKM can be regarded as a simultaneous pattern classifier and associator. In the simulation study for pattern classification, it is justified that an SSKM consisting of distinct kernel networks can yield relatively compact-sized pattern classifiers, while preserving a reasonably high generalization capability, in comparison with the approach using support vector machines (SVMs).

In this paper, a dynamic neurocontroller for positioning of robots based on static and parametric neural networks (NNs) has been developed. This controller is based on Christoffel symbols of first kind in order to carry out coriolis/centripetal matrix. Structural properties of robots and Kronecker product has been taken into account to develop NNs to approximate nonlinearities. The weight updating laws have been obtained from a nonlinear strategy based on Lyapunov energy that guarantees both stability and boundedness of signals and weights. The NN weights are tuned online with no "offline learning phase" and are initialized to zero. The neurocontroller improves the implementation with respect to other dynamic NNs used in the literature.

In this letter, we comment on "Pruning Error Minimization in Least Squares Support Vector Machines" by B. J. de Kruif and T. J. A. de Vries. The original paper proposes a way of pruning training examples for least squares support vector machines (LS SVM) using no regularization (-gamma = infinity). This causes a problem as the derivation involves inverting a matrix that is often singular. We discuss a modification of this algorithm that prunes with regularization (gamma finite and nonzero) and is also computationally more efficient.

While distance function learning for supervised learning tasks has a long history, extending it to learning tasks with weaker supervisory information has only been studied recently. In particular, some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information. In this paper, we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach. The metric learning problem is thus formulated as an optimization problem for kernel learning. An attractive property of the optimization problem is that it is convex and, hence, has no local optima. While a closed-form solution exists for the first special case, the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically. Experimental results based on both synthetic and real-world data show that this new kernel approach is promising for nonlinear metric learning.

This paper presents a new classifier called total margin-based adaptive fuzzy support vector machines (TAF-SVM) that deals with several problems that may occur in support vector machines (SVMs) when applied to the face recognition. The proposed TAF-SVM not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty, but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm. In addition, by introducing the total margin algorithm to replace the conventional soft margin algorithm, a lower generalization error bound can be obtained. Those three functions are embodied into the traditional SVM so that the TAF-SVM is proposed and reformulated in both linear and nonlinear cases. By using two databases, the Chung Yuan Christian University (CYCU) multiview and the facial recognition technology (FERET) face databases, and using the kernel Fisher's discriminant analysis (KFDA) algorithm to extract discriminating face features, experimental results show that the proposed TAF-SVM is superior to SVM in terms of the face-recognition accuracy. The results also indicate that the proposed TAF-SVM can achieve smaller error variances than SVM over a number of tests such that better recognition stability can be obtained.

The Akaike information criterion (AIC) is a widely used tool for model selection. AIC is derived as an asymptotically unbiased estimator of a function used for ranking candidate models which is a variant of the Kullback-Leibler divergence between the true model and the approximating candidate model. Despite the Kullback-Leibler's computational and theoretical advantages, what can become inconvenient in model selection applications is their lack of symmetry. Simple examples can show that reversing the role of the arguments in the Kullback-Leibler divergence can yield substantially different results. In this paper, three new functions for ranking candidate models are proposed. These functions are constructed by symmetrizing the Kullback-Leibler divergence between the true model and the approximating candidate model. The operations used for symmetrizing are the average, geometric, and harmonic means. It is found that the original AIC criterion is an asymptotically unbiased estimator of these three different functions. Using one of these proposed ranking functions, an example of new bias correction to AIC is derived for univariate linear regression models. A simulation study based on polynomial regression is provided to compare the different proposed ranking functions with AIC and the new derived correction with AICc.

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lstrokojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lstrokojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: 1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; 2) for convex QP problems, the same result as in 1) holds; moreover, the singleton belongs to the set of global minimizers; and 3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points

Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables.

Decomposition methods are currently one of the major methods for training support vector machines. They vary mainly according to different working set selections. Existing implementations and analysis usually consider some specific selection rules. This paper studies sequential minimal optimization type decomposition methods under a general and flexible way of choosing the two-element working set. The main results include: 1) a simple asymptotic convergence proof, 2) a general explanation of the shrinking and caching techniques, and 3) the linear convergence of the methods. Extensions to some support vector machine variants are also discussed.

The kernel function plays a central role in kernel methods. Most existing methods can only adapt the kernel parameters or the kernel matrix based on empirical data. Recently, Ong et al. introduced the method of hyperkernels which can be used to learn the kernel function directly in an inductive setting. However, the associated optimization problem is a semidefinite program (SDP), which is very computationally expensive, even with the recent advances in interior point methods. In this paper, we show that this learning problem can be equivalently reformulated as a second-order cone program (SOCP), which can then be solved more efficiently than SDPs. Comparison is also made with the kernel matrix learning method proposed by Lanckriet et al. Experimental results on both classification and regression problems, with toy and real-world data sets, show that our proposed SOCP formulation has significant speedup over the original SDP formulation. Moreover, it yields better generalization than Lanckriet et al.'s method, with a speed that is comparable, or sometimes even faster, than their quadratically constrained quadratic program (QCQP) formulation.

Solutions of least squares support vector machines (LS-SVMs) are typically nonsparse. The sparseness is imposed by subsequently omitting data that introduce the smallest training errors and retraining the remaining data. Iterative retraining requires more intensive computations than training a single nonsparse LS-SVM. In this paper, we propose a new pruning algorithm for sparse LS-SVMs: the sequential minimal optimization (SMO) method is introduced into pruning process; in addition, instead of determining the pruning points by errors, we omit the data points that will introduce minimum changes to a dual objective function. This new criterion is computationally efficient. The effectiveness of the proposed method in terms of computational cost and classification accuracy is demonstrated by numerical experiments.

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.

This paper proposes a complete framework of posterior probability support vector machines (PPSVMs) for weighted training samples using modified concepts of risks, linear separability, margin, and optimal hyperplane. Within this framework, a new optimization problem for unbalanced classification problems is formulated and a new concept of support vectors established. Furthermore, a soft PPSVM with an interpretable parameter /spl nu/ is obtained which is similar to the /spl nu/-SVM developed by Scho/spl uml/lkopf et al., and an empirical method for determining the posterior probability is proposed as a new approach to determine /spl nu/. The main advantage of an PPSVM classifier lies in that fact that it is closer to the Bayes optimal without knowing the distributions. To validate the proposed method, two synthetic classification examples are used to illustrate the logical correctness of PPSVMs and their relationship to regular SVMs and Bayesian methods. Several other classification experiments are conducted to demonstrate that the performance of PPSVMs is better than regular SVMs in some cases. Compared with fuzzy support vector machines (FSVMs), the proposed PPSVM is a natural and an analytical extension of regular SVMs based on the statistical learning theory.

This paper considers the problem of robust exponential /spl epsiv/-regulation for a class of multi-input nonlinear systems with uncertainties. The uncertainties appear not only in the feedback channel but also in the control channel. Under some mild assumptions, an adaptive neural network control scheme is developed such that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded and, under the control scheme with initial data starting in some compact set, the states of the closed-loop system is guaranteed to exponentially converge to an arbitrarily specified /spl epsi/-neighborhood about the origin. The important contributions of the present work are that a new exponential uniformly ultimately bounded performance is proposed and that the design parameters and initial condition set can be determined easily. The development generalizes and improves earlier results for the single-input case.

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.

In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.

We consider a class of nonlinear models based on mixtures of local autoregressive time series. At any given time point, we have a certain number of linear models, denoted as experts, where the vector of covariates may include lags of the dependent variable. Additionally, we assume the existence of a latent multinomial variable, whose distribution depends on the same covariates as the experts, that determines which linear process is observed. This structure, denoted as mixture-of-experts (ME), is considerably flexible in modeling the conditional mean function, as shown by Jiang and Tanner. In this paper, we present a formal treatment of conditions to guarantee the asymptotic normality of the maximum likelihood estimator (MLE), under stationarity and nonstationarity, and under correct model specification and model misspecification. The performance of common model selection criteria in selecting the number of experts is explored via Monte Carlo simulations. Finally, we present applications to simulated and real data sets, to illustrate the ability of the proposed structure to model not only the conditional mean, but also the whole conditional density.

This paper presents an asymmetric subsethood-product fuzzy neural inference system (ASuPFuNIS) that directly extends the SuPFuNIS model by permitting signal and weight fuzzy sets to be modeled by asymmetric Gaussian membership functions. The asymmetric subsethood-product network admits both numeric as well as linguistic inputs. Input nodes, which act as tunable feature fuzzifiers, fuzzify numeric inputs with asymmetric Gaussian fuzzy sets; and linguistic inputs are presented as is. The antecedent and consequent labels of standard fuzzy if-then rules are represented as asymmetric Gaussian fuzzy connection weights of the network. The model uses mutual subsethood based activation spread and a product aggregation operator that works in conjunction with volume defuzzification in a gradient descent learning framework. Despite the increase in the number of free parameters, the proposed model performs better than SuPFuNIS, on various benchmarking problems, both in terms of the performance accuracy and architectural economy and compares excellently with other various existing models with a performance better than most of them.

In this paper, we present a gradient ascent learning method of the Hopfield neural network for bipartite subgraph problem. The method is intended to provide a near-optimum parallel algorithm for solving the bipartite subgraph problem. To do this we use the Hopfield neural network to get a near-maximum bipartite subgraph, and increase the energy by modifying weights in a gradient ascent direction of the energy to help the network escape from the state of the near-maximum bipartite subgraph to the state of the maximum bipartite subgraph or better one. A large number of instances are simulated to verify the proposed method with the simulation results showing that the solution quality is superior to that of best existing parallel algorithm. We also test the learning method on total coloring problem. The simulation results show that our method finds optimal solution in every test graph.

In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is noniterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Evaluations on performing kernel PCA and kernel clustering on the USPS data set show much improved performance.