Search

This paper proposes neural organization of generalized adalines (gadalines) for data driven function approximation. By generalizing the threshold function of adalines, we achieve the K-state transfer function of gadalines which responds a unitary vector of K binary values to the projection of a predictor on a receptive field. A generative component that uses the K-state activation of a gadaline to trigger K posterior independent normal variables is employed to emulate stochastic predictor-oriented target generation. The fitness of a generative component to a set of paired data mathematically translates to a mixed integer and linear programming. Since consisting of continuous and discrete variables, the mathematical framework is resolved by a hybrid of the mean field annealing and gradient descent methods. Following the leave-one-out learning strategy, the obtained learning method is extended for optimizing multiple generative components. The learning result leads to parameters of a deterministic gadaline network for function approximation. Numerical simulations further test the proposed learning method with paired data oriented from a variety of target functions. The result shows that the proposed learning method outperforms the MLP and RBF learning methods for data driven function approximation.

In this paper, adaptive neural network (NN) control is investigated for a class of discrete-time multi-input-multi-output (MIMO) nonlinear systems with triangular form inputs. Each subsystem of the MIMO system is in strict feedback form. First, through two phases of coordinate transformation, the MIMO system is transformed into input-output representation with the triangular form input structure unchanged. By using high-order neural networks (HONNs) as the emulators of the desired controls, effective output feedback adaptive control is developed using backstepping. The closed-loop system is proved to be semiglobally uniformly ultimate bounded (SGUUB) by using Lyapunov method. The output tracking errors are guaranteed to converge into a compact set whose size is adjustable, and all the other signals in the closed-loop system are proved to be bounded. Simulation results show the effectiveness of the proposed control scheme.

The solution of partial differential equations (PDE) arises in a wide variety of engineering problems. Solutions to most practical problems use numerical analysis techniques such as finite-element or finite-difference methods. The drawbacks of these approaches include computational costs associated with the modeling of complex geometries. This paper proposes a finite-element neural network (FENN) obtained by embedding a finite-element model in a neural network architecture that enables fast and accurate solution of the forward problem. Results of applying the FENN to several simple electromagnetic forward and inverse problems are presented. Initial results indicate that the FENN performance as a forward model is comparable to that of the conventional finite-element method (FEM). The FENN can also be used in an iterative approach to solve inverse problems associated with the PDE. Results showing the ability of the FENN to solve the inverse problem given the measured signal are also presented. The parallel nature of the FENN also makes it an attractive solution for parallel implementation in hardware and software.

Support vector machine (SVM) learning has been recently proposed for image compression in the frequency domain using a constant epsilon-insensitivity zone by Robinson and Kecman. However, according to the statistical properties of natural images and the properties of human perception, a constant insensitivity makes sense in the spatial domain but it is certainly not a good option in a frequency domain. In fact, in their approach, they made a fixed low-pass assumption as the number of discrete cosine transform (DCT) coefficients to be used in the training was limited. This paper extends the work of Robinson and Kecman by proposing the use of adaptive insensitivity SVMs [2] for image coding using an appropriate distortion criterion [3], [4] based on a simple visual cortex model. Training the SVM by using an accurate perception model avoids any a priori assumption and improves the rate-distortion performance of the original approach.

Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the sufficient and necessary conditions of the solution, this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints. Three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of Lyapunov and converges to an exact solution of the original problem. Meanwhile, the proposed network with a gradient mapping is also proved to be stable in the sense of Lyapunov and to have a finite-time convergence under some mild conditions by using a new energy function. Compared with the existing neural networks, the new model can be applied to solve some nonmonotone problems, has no adjustable parameter, and has lower complexity. Thus, the structure of the proposed network is very simple. Since the proposed network can be used to solve a broad class of optimization problems, it has great application potential. The validity and transient behavior of the proposed neural network are demonstrated by several numerical examples.

In this paper, we consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the self-exciting threshold autoregressive (SETAR), the autoregressive neural network (AR-NN), and the logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, our formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models. A model building procedure is developed based on statistical inference arguments. A Monte Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This paper presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.

This paper proposes a novel cross-correlation neural network (CNN) model for finding the principal singular subspace of a cross-correlation matrix between two high-dimensional data streams. We introduce a novel nonquadratic criterion (NQC) for searching the optimum weights of two linear neural networks (LNN). The NQC exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix, respectively. The other stationary points of the NQC are (unstable) saddle points. We develop an adaptive algorithm based on the NQC for tracking the principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences. The NQC algorithm provides a fast online learning of the optimum weights for two LNN. The global asymptotic stability of the NQC algorithm is analyzed. The NQC algorithm has several key advantages such as faster convergence, which is illustrated through simulations.

This paper derives a family of differential learning rules that optimize the Shannon entropy at the output of an adaptive system via kernel density estimation. In contrast to parametric formulations of entropy, this nonparametric approach assumes no particular functional form of the output density. We address problems associated with quantized data and finite sample size, and implement efficient maximum likelihood techniques for optimizing the regularizer. We also develop a normalized entropy estimate that is invariant with respect to affine transformations, facilitating optimization of the shape, rather than the scale, of the output density. Kernel density estimates are smooth and differentiable; this makes the derived entropy estimates amenable to manipulation by gradient descent. The resulting weight updates are surprisingly simple and efficient learning rules that operate on pairs of input samples. They can be tuned for data-limited or memory-limited situations, or modified to give a fully online implementation.

In this paper, we introduce a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following the proposed approach, the blind signal separation framework can be posed as a nonlinear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. We conducted a series of Monte Carlo simulations, involving linear mixtures of various source signals with different statistical characteristics and sample sizes. The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics, can consistently achieve an accurate separation of all the mixed signals. 2) Adopting a suitably designed optimization framework, it is possible to derive a flexible ICA algorithm that matches the stability and convergence properties of conventional algorithms. 3) A nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions.

In the last few years, the support vector machine (SVM) method has motivated new interest in kernel regression techniques. Although the SVM has been shown to exhibit excellent generalization properties in many experiments, it suffers from several drawbacks, both of a theoretical and a technical nature: the absence of probabilistic outputs, the restriction to Mercer kernels, and the steep growth of the number of support vectors with increasing size of the training set. In this paper, we present a different class of kernel regressors that effectively overcome the above problems. We call this approach generalized LASSO regression. It has a clear probabilistic interpretation, can handle learning sets that are corrupted by outliers, produces extremely sparse solutions, and is capable of dealing with large-scale problems. For regression functionals which can be modeled as iteratively reweighted least-squares (IRLS) problems, we present a highly efficient algorithm with guaranteed global convergence. This defies a unique framework for sparse regression models in the very rich class of IRLS models, including various types of robust regression models and logistic regression. Performance studies for many standard benchmark datasets effectively demonstrate the advantages of this model over related approaches.

A key step of using gradient descend methods to develop learning algorithms of a regular feedforward fuzzy neural network (FNN) is to differentiate max-min functions, which contain max(/spl or/) and min(/spl and/) operations. The paper aims at several objectives. First, investigate further the differentiation of /spl or/-/spl and/ functions. Second, employ general fuzzy numbers, which include triangular and trapezoidal fuzzy numbers as special cases to define a three-layer regular FNN. The general fuzzy numbers related can be approximately determined by their corresponding finite level sets. So, we can approximately represent the input-output (I/O) relationship of the regular FNN as functions of the endpoints of all finite level sets. Third, a fuzzy back-propagation algorithm is presented. And to speed up the convergence of the learning algorithm, a fuzzy conjugate gradient algorithm for fuzzy weights and biases is developed, furthermore, the convergence of the algorithm is analyzed, systematically. Finally, some real simulations demonstrate the efficiency of our learning algorithms. The regular FNN is applied to the approximate realization of fuzzy inference rules and fuzzy functions defined on given compact sets.

The problem of finding all cycles in the exponentially growing state space of synchronous Boolean networks was studied in the paper by C. Farrow, J. Heidel, J. Maloney, and J. R. Scalar, "Equations for synchronous Boolean networks with biological applications," IEEE trans. Neural Networks, vol. 15, no. 2, pp. 348-354 Mar. 2004. No efficient algorithm was given to solve the problem. We show that even the determination of the number of fixed points (cycles of length 1) for monotone Boolean networks and the determination of the existence of fixed points for general Boolean networks are both strong NP-complete.