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In this paper, we propose a new feature extraction method for feedforward neural networks. The method is based on the recently published decision boundary feature extraction algorithm which is based on the fact that all the necessary features for classification can be extracted from the decision boundary. The decision boundary feature extraction algorithm can take advantage of characteristics of neural networks which can solve complex problems with arbitrary decision boundaries without assuming underlying probability distribution functions of the data. To apply the decision boundary feature extraction method, we first give a specific definition for the decision boundary in a neural network. Then, we propose a procedure for extracting all the necessary features for classification from the decision boundary. Experiments show promising results.

The design problem of generalized brain-state-in-a-box (GBSB) type associative memories is formulated as a constrained optimization program, and "designer" neural networks for solving the program in real time are proposed. The stability of the designer networks is analyzed using Barbalat's lemma. The analyzed and synthesized neural associative memories do not require symmetric weight matrices. Two types of the GBSB-based associative memories are analyzed, one when the network trajectories are constrained to reside in the hypercube [-1, 1](n) and the other type when the network trajectories are confined to stay in the hypercube [0, 1](n). Numerical examples and simulations are presented to illustrate the results obtained.

Learning and convergence properties of linear threshold elements or perceptrons are well understood for the case where the input vectors (or the training sets) to the perceptron are linearly separable. Little is known, however, about the behavior of the perceptron learning algorithm when the training sets are linearly nonseparable. We present the first known results on the structure of linearly nonseparable training sets and on the behavior of perceptrons when the set of input vectors is linearly nonseparable. More precisely, we show that using the well known perceptron learning algorithm, a linear threshold element can learn the input vectors that are provably learnable, and identify those vectors that cannot be learned without committing errors. We also show how a linear threshold element can be used to learn large linearly separable subsets of any given nonseparable training set. In order to develop our results, we first establish formal characterizations of linearly nonseparable training sets and define learnable structures for such patterns. We also prove computational complexity results for the related learning problems. Next, based on such characterizations, we show that a perceptron does the best one can expect for linearly nonseparable sets of input vectors and learns as much as is theoretically possible.

In this paper we study three different classes of neural network models for solving linear programming problems. We investigate the following characteristics of each model: model complexity, complexity of individual neurons, and accuracy of solutions. Simulation examples are given to illustrate the dynamical behavior of each model.

Parallel, self-organizing, hierarchical neural networks (PSHNN's) are multistage networks in which stages operate in parallel rather than in series during testing. Each stage can be any particular type of network. Previous PSHNN's assume quantized, say, binary outputs. A new type of PSHNN is discussed such that the outputs are allowed to be continuous-valued. The performance of the resulting networks is tested in the problem of predicting speech signal samples from past samples. Three types of networks in which the stages are learned by the delta rule, sequential least-squares, and the backpropagation (BP) algorithm, respectively, are described. In all cases studied, the new networks achieve better performance than linear prediction. A revised BP algorithm is discussed for learning input nonlinearities. When the BP algorithm is to be used, better performance is achieved when a single BP network is replaced by a PSHNN of equal complexity in which each stage is a BP network of smaller complexity than the single BP network.

In this work, the authors propose a novel method to obtain correspondence between range data across image frames using neural like mechanisms. The method is computationally efficient and tolerant of noise and missing points. Elastic nets, which evolved out of research into mechanisms to establish ordered neural projections between structures of similar geometry, are used to cast correspondence as an optimization problem. This formulation is then used to obtain approximations to the motion parameters under the assumption of rigidity (inelasticity). These parameter scan be used to recover correspondence. Experimental results are presented to establish the veracity of the scheme and the method is compared to earlier attempts in this direction.

A study of the memory characteristics of the brain and the computer prompts the creation of a new neuron architecture for neural computation. We hypothesize that neural responses resemble hysteresis loops. The upper and lower halves of the hysteresis loop are described by two sigmoids. Generalizing the two sigmoids to two families of curves accommodates loops of various sizes. This model, which we call the ;hystery model', is capable of memorizing the entire history of its bipolar inputs in an adaptive fashion, with larger memory for longer sequences. We theorize and prove that the hystery model's response converges asymptotically to hysteresis-like loops. A simple application to temporal pattern discrimination demonstrates the nonlinear short-term memory characteristics of the hystery model. This model may have important applications for time-based computations such as control, signal processing and spatiotemporal pattern recognition, especially if it can take advantage of existing hysteresis phenomena in semiconductor materials.

This paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network (RBFNN). After a nonparametric approximate model of the system is constructed from a priori experiments or simulations, a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations. The procedures for both training and state estimation are described along with discussions on approximation error. Nonlinear systems with linear output equations are considered as a special case of the general formulation. Finally, applications of the proposed RBFNN to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method.

A neural network inverse dynamics controller with adjustable weights is compared with a computed-torque type adaptive controller. Lyapunov stability techniques, usually applied to adaptive systems, are used to derive a globally asymptotically stable adaptation law for a single-layer neural network controller that bears similarities to the well-known delta rule for neural networks. This alternative learning rule allows the learning rates of each connection weight to be individually adjusted to give faster convergence. The role of persistently exciting inputs in ensuring parameter convergence, often mentioned in the context of adaptive systems, is emphasized in relation to the convergence of neural network weights. A coupled, compound pendulum system is used to develop inverse dynamics controllers based on adaptive and neural network techniques. Adaptation performance is compared for a model-based adaptive controller and a simple neural network utilizing both delta-rule learning and the alternative adaptation law.

The ideal use of small multilayer nets at the decision nodes of a binary classification tree to extract nonlinear features is proposed. The nets are trained and the tree is grown using a gradient-type learning algorithm in the multiclass case. The method improves on standard classification tree design methods in that it generally produces trees with lower error rates and fewer nodes. It also reduces the problems associated with training large unstructured nets and transfers the problem of selecting the size of the net to the simpler problem of finding a tree of the right size. An efficient tree pruning algorithm is proposed for this purpose. Trees constructed with the method and the CART method are compared on a waveform recognition problem and a handwritten character recognition problem. The approach demonstrates significant decrease in error rate and tree size. It also yields comparable error rates and shorter training times than a large multilayer net trained with backpropagation on the same problems.

The authors present a new training algorithm to be used on a four-layer perceptron-type feedforward neural network for the generation of binary-to-binary mappings. This algorithm is called the Boolean-like training algorithm (BLTA) and is derived from original principles of Boolean algebra followed by selected extensions. The algorithm can be implemented on analog hardware, using a four-layer binary feedforward neural network (BFNN). The BLTA does not constitute a traditional circuit building technique. Indeed, the rules which govern the BLTA allow for generalization of data in the face of incompletely specified Boolean functions. When compared with techniques which employ descent methods, training times are greatly reduced in the case of the BLTA. Also, when the BFNN is used in conjunction with A/D converters, the applicability of the present algorithm can be extended to accept real-valued inputs.

A new neural-network architecture called the parallel, self-organizing, hierarchical neural network (PSHNN) is presented. The new architecture involves a number of stages in which each stage can be a particular neural network (SNN). At the end of each stage, error detection is carried out, and a number of input vectors are rejected. Between two stages there is a nonlinear transformation of input vectors rejected by the previous stage. The new architecture has many desirable properties, such as optimized system complexity (in the sense of minimized self-organizing number of stages), high classification accuracy, minimized learning and recall times, and truly parallel architectures in which all stages operate simultaneously without waiting for data from other stages during testing. The experiments performed indicated the superiority of the new architecture over multilayered networks with back-propagation training.

A new algorithm called the self-organizing neural network (SONN) is introduced. Its use is demonstrated in a system identification task. The algorithm constructs a network, chooses the node functions, and adjusts the weights. It is compared to the backpropagation algorithm in the identification of the chaotic time series. The results show that SONN constructs a simpler, more accurate model, requiring less training data and fewer epochs. The algorithm can also be applied as a classifier.