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ADAPTIVE algorithms WITH NONLINEAR DATA AND ERROR FUNCTIONS

IEEE TRANSACTIONS ON SIGNAL PROCESSING 1992年第9期40卷 2199-2206页

作者： SETHARES, WA Department of Electrical and Computer Engineering University of Wisconsin Madison Madison WI USA

Using the tools of nonlinear system theory, we examine several common nonlinear variants of the LMS algorithm and derive a persistence of excitation criteria for local exponential stability. The condition is tight when the inputs are periodic, and a generic counterexample is demonstrated which gives (local) instability for a large class of such nonlinear versions of LMS, specifically, those which utilize a nonlinear data function. The presence of a nonlinear error function is found to be relatively benign in that it does not affect the stability of the error system. Rather, it defines the cost function the algorithm tends to minimize. Specific examples include the dead zone modification, the cubed data nonlinearity, the cubed error nonlinearity, the signed regressor algorithm, and a single layer version of the backpropagation algorithm.

关键词： Adaptive algorithm Least squares approximation Cost function backpropagation algorithms Nonlinear systems Convergence Adaptive systems Stability criteria Signal generators

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SELF-TUNING OF COMPUTED TORQUE GAINS BY USING NEURAL NETWORKS WITH FLEXIBLE STRUCTURES

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 1994年第4期141卷 235-242页

作者： TESHNEHLAB, M WATANABE, K SAGA UNIV FAC SCI & ENGNDEPT MECH ENGNSAGA 840JAPAN

The paper principally describes the design of an artificial neural network using flexible sigmoid unit functions (FSUFs), referred to as flexible sigmoid function networks (FSFNs), to achieve both a high flexibility and a high learning ability in neural network structures from a given set of teaching patterns. An FSFN can generate an appropriate shape of the sigmoid function for each of the individual hidden- and output-layer units, in accordance with the specified inputs, desired output(s) and applied system. The paper proposes a learning method in which not only connection weights but also the sigmoid functions may be adjusted. The learning algorithm is derived by using the well known back-propagation algorithm. To demonstrate the validity of the proposed method, we apply the FSFN to the construction of a self-tuning computed torque controller for a two-link manipulator. It is then shown that the controller based on the FSFN gives a better control performance than that based on the traditional neural network.

关键词： backpropagation algorithms COMPUTED TORQUE CONTROL FLEXIBLE SIGMOID FUNCTIONS NEURAL NETWORKS SELF-TUNING CONTROL

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ADJUNCTS AND ALTERNATIVES TO NEURAL NETWORKS FOR SUPERVISED CLASSIFICATION

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS 1992年第1期22卷 35-46页

作者： GYER, MS Eclectics Inc. Tucson AZ USA

While multilayer neural networks (NN's) are a powerful tool for supervised classification their intrinsic nonlinearity often leads to slow convergence or divergence when the training sets include multimodal and/or overlapping classes. Well known optimization techniques improves classification performance and convergence rate and reduces the tendency for divergence. Optimization techniques are also applied to the development of a noniterative perceptron-like algorithm, called vector valued perceptrons (VVP). A comparison of the VVP and the backpropagation (BP) algorithms for supervised classification indicates that the performance of VVP's is comparable to BP. VVP's are capable of solving multiclass classification problems such as the exclusive-or problem, but require significantly less time (by as much as several orders of magnitude) than BP. This is especially the case for sample data with overlapping classes where BP may converge very slowly, perform poorly or diverge. VVP's applied as an adjunct and preprocessor for NN's in such cases result in improved NN classification performance and reduction in computational time.

关键词： Neural networks Convergence Nonhomogeneous media Vectors Multi-layer neural network backpropagation algorithms Classification algorithms Sensor systems Training data

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A FAST NEW ALGORITHM FOR TRAINING FEEDFORWARD NEURAL NETWORKS

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1992年第1期40卷 202-210页

作者： SCALERO, RS TEPEDELENLIOGLU, N FLORIDA INST TECHNOL DEPT ELECT & COMP ENGNMELBOURNEFL 32901

A fast new algorithm is presented for training multilayer perceptrons as an alternative to the backpropagation algorithm. The number of iterations required by the new algorithm to converge is less than 20% of what is required by the backpropagation algorithm. Also, it is less affected by the choice of initial weights and setup parameters. The algorithm uses a modified form of the backpropagation algorithm to minimize the mean-squared error between the desired and actual outputs with respect to the inputs to the nonlinearities. This is in contrast to the standard algorithm which minimizes the mean-squared error with respect to the weights. Error signals, generated by the modified backpropagation algorithm, are used to estimate the inputs to the nonlinearities, which along with the input vectors to the respective nodes, are used to produce an updated set of weights through a system of linear equations at each node. These systems of linear equations are solved using a Kalman filter at each layer.

关键词： Neural networks Feedforward neural networks backpropagation algorithms Signal generators Vectors Iterative algorithms Linearity Error correction Nonlinear equations Speech

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Optimal control of terminal processes using neural networks

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1996年第2期7卷 408-418页

作者： Plumer, ES Los Alamos National Laboratory Los Alamos NM USA

Feedforward neural networks are capable of approximating continuous multivariate functions and, as such, can implement nonlinear state-feedback controllers. Training methods such as backpropagation-through-time (BPTT), however, do not deal with terminal control problems in which the specified cost function includes the elapsed trajectory-time. In this paper, an extension to BPTT is proposed which addresses this limitation, The controller design is reformulated as a constrained optimization problem defined over the entire field of extremals and in which the set of trajectory times is incorporated into the cost function. Necessary first-order stationary conditions are derived which correspond to standard BPTT with the addition of certain transversality conditions. The new gradient algorithm based on these conditions, called time-optimal backpropagation through time (TOBPTT), is tested on two benchmark minimum-time control problems.

关键词： Optimal control Neural networks Open loop systems Cost function Regulators Feedforward neural networks Constraint optimization Design optimization backpropagation algorithms Nonlinear control systems

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GRADIENT CALCULATIONS FOR DYNAMIC RECURRENT NEURAL NETWORKS - A SURVEY

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1995年第5期6卷 1212-1228页

作者： PEARLMUTTER, BA Learning Systems Department Siemens AG Corporate Research and Development Princeton NJ USA

We survey learning algorithms for recurrent neural networks with hidden units and put the various techniques into a common framework, We discuss fixed point learning algorithms, namely recurrent backpropagation and deterministic Boltzmann machines, and nonfixed point algorithms, namely backpropagation through time, Elman's history cutoff, and Jordan's output feedback architecture, Forward propagation, an on-line technique that uses adjoint equations, and variations thereof, are also discussed, In many cases, the unified presentation leads to generalizations of various sorts, We discuss advantages and disadvantages of temporally continuous neural networks in contrast to clocked ones continue with some ''tricks of the trade'' for training, using, and simulating continuous time and recurrent neural networks, We present some simulations, and at the end, address issues of computational complexity and learning speed.

关键词： Recurrent neural networks backpropagation algorithms Computational modeling Machine learning History Output feedback Equations Neural networks Clocks Computational complexity

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HIDDEN CONTROL NEURAL ARCHITECTURE MODELING OF NONLINEAR TIME-VARYING SYSTEMS AND ITS APPLICATIONS

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1993年第1期4卷 109-116页

作者： LEVIN, E Speech Research Department AT and T Bell Laboratories Inc. Murray Hill NJ USA

Multilayered neural networks have been proposed recently for nonlinear prediction and system modeling [1]-[6]. Although neural networks have *** for modeling time invariant nonlinear systems, it has been difficult to apply them to complicated nonstationary signals, such as speech because they are unable to characterize temporal variability. In this paper we address this problem by proposing a network architecture, called ''hidden control neural network'' (HCNN) [4], for modeling signals generated by nonlinear dynamical systems with restricted time variability. Our approach is to allow the mapping that is implemented by a multilayered neural network to change with time as a function of an additional control input signal. This network is trained using an algorithm that is based on ''back-propagation'' and segmentation algorithms for estimating the unknown control together with the network's parameters. This network wa$ applied to three different tasks: segmentation and modeling of a signal produced by a time-varying nonlinear system;speaker-independent recognition of spoken connected digit;and on-line recognition of handwritten characters. The results of these experiments demonstrate the ability of HCNN to learn time-varying nonlinear dynamics, and its potential for high performance recognition of signals, produced by time-varying sources, such as spoken utterances, and written characters.

关键词： Neural networks Time varying systems Character recognition Handwriting recognition Nonlinear systems Nonlinear dynamical systems backpropagation algorithms Speech Nonlinear control systems Signal generators

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A HYBRID ALGORITHM FOR DETERMINING PROTEIN-STRUCTURE

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IEEE EXPERT-INTELLIGENT SYSTEMS & THEIR APPLICATIONS 1994年第4期9卷 66-74页

作者： ZYHANG, X One Cambridge Center PHZ Partners Cambridge MA

At Thinking Machines, my colleagues and I have developed a hybrid system combining a neural network, a statistical module, and a memory-based reasoner, each of which makes its own prediction. A combiner then blends these results to produce the final predictions. This hybrid system improves its ability to determine how amino acid sequences fold into 3D protein structures. It predicts secondary structures with 66.4% accuracy. Both the neural network and the combiner are multilayer perceptrons trained with the standard backpropagation algorithm; this article focuses on the other two components, and on how we trained the hybrid system and used it for prediction. I also discuss how future work in AI and other sciences might meet the challenge of the protein folding problem.

关键词： Proteins Neural networks Amino acids Multi-layer neural network Multilayer perceptrons backpropagation algorithms Artificial intelligence

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Integrated feature and architecture selection

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1996年第4期7卷 1007-1014页

作者： Steppe, JM Bauer, KW Rogers, SK USAF INST TECHNOL DEPT ELECT & COMP ENGN WRIGHT PATTERSON AFB OH 45433 USA

In this paper, we present an integrated approach to feature and architecture selection for single hidden layer-feedforward neural networks trained via backpropagation. In our approach, we adopt a statistical model building perspective in which we analyze neural networks within a nonlinear regression framework, The algorithm presented in this paper employs a likelihood-ratio test statistic as a model selection criterion, This criterion is used in a sequential procedure aimed at selecting the best neural network given an initial architecture as determined by heuristic rules, Application results for an object recognition problem demonstrate the selection algorithm's effectiveness in identifying reduced neural networks with equivalent prediction accuracy.

关键词： Neural networks Buildings Feedforward neural networks Testing backpropagation algorithms Statistical analysis Object recognition Accuracy Multi-layer neural network Military computing

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AN IMPROVED ALGORITHM FOR NEURAL-NETWORK CLASSIFICATION OF IMBALANCED TRAINING SETS

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1993年第6期4卷 962-969页

作者： ANAND, R MEHROTRA, KG MOHAN, CK RANKA, S SYRACUSE UNIV SCH COMP & INFORMAT SCISYRACUSENY 13244

The backpropagation algorithm converges very slowly for two-class problems in which most of the exemplars belong to one dominant class. We analyze that this occurs because the computed net error gradient vector is dominated by the bigger class so much that the net error for the exemplars in the smaller class increases significantly in the initial iteration. The subsequent rate of convergence of the net error is very low. We present a modified technique for calculating a direction in weight-space which decreases the error for each class. Using this algorithm, we have been able to accelerate the rate of learning for two-class classification problems by an order of magnitude.

关键词： Neural networks backpropagation algorithms Convergence Acceleration Information science Algorithm design and analysis

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