Showing papers in "IEEE Transactions on Neural Networks in 1998"
TL;DR: This article illustrates the method by solving a variety of model problems and presents comparisons with solutions obtained using the Galekrkin finite element method for several cases of partial differential equations.
Abstract: We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial/boundary conditions. This part involves a feedforward neural network containing adjustable parameters (the weights). Hence by construction the initial/boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ordinary differential equations (ODE), to systems of coupled ODE and also to partial differential equations (PDE). In this article, we illustrate the method by solving a variety of model problems and present comparisons with solutions obtained using the Galerkin finite element method for several cases of partial differential equations. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.
1,459 citations
TL;DR: A combined kinematic/torque control law is developed using backstepping and stability is guaranteed by Lyapunov theory, which can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following, and stabilization about a desired posture.
Abstract: A control structure that makes possible the integration of a kinematic controller and a neural network (NN) computed-torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping and stability is guaranteed by Lyapunov theory. This control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following, and stabilization about a desired posture. Moreover, the NN controller proposed in this work can deal with unmodeled bounded disturbances and/or unstructured unmodeled dynamics in the vehicle. Online NN weight tuning algorithms do not require off-line learning yet guarantee small tracking errors and bounded control signals are utilized.
694 citations
TL;DR: Instead of training convolutional networks by time-consuming error backpropagation, a modular procedure is applied whereby layers are trained sequentially from the input to the output layer in order to recognize features of increasing complexity.
Abstract: Convolutional neural networks provide an efficient method to constrain the complexity of feedforward neural networks by weight sharing and restriction to local connections. This network topology has been applied in particular to image classification when sophisticated preprocessing is to be avoided and raw images are to be classified directly. In this paper two variations of convolutional networks-neocognitron and a modification of neocognitron-are compared with classifiers based on fully connected feedforward layers with respect to their visual recognition performance. For a quantitative experimental comparison with standard classifiers two very different recognition tasks have been-chosen: handwritten digit recognition and face recognition. In the first example, the generalization of convolutional networks is compared to fully connected networks; in the second example human face recognition is investigated under constrained and variable conditions, and the limitations of convolutional networks are discussed.
612 citations
TL;DR: This paper rigorously proves that standard single-hidden layer feedforward networks with at most N hidden neurons and with any bounded nonlinear activation function which has a limit at one infinity can learn N distinct samples with zero error.
Abstract: It is well known that standard single-hidden layer feedforward networks (SLFNs) with at most N hidden neurons (including biases) can learn N distinct samples (x/sub i/,t/sub i/) with zero error, and the weights connecting the input neurons and the hidden neurons can be chosen "almost" arbitrarily. However, these results have been obtained for the case when the activation function for the hidden neurons is the signum function. This paper rigorously proves that standard single-hidden layer feedforward networks (SLFNs) with at most N hidden neurons and with any bounded nonlinear activation function which has a limit at one infinity can learn N distinct samples (x/sub i/,t/sub i/) with zero error. The previous method of arbitrarily choosing weights is not feasible for any SLFN. The proof of our result is constructive and thus gives a method to directly find the weights of the standard SLFNs with any such bounded nonlinear activation function as opposed to iterative training algorithms in the literature.
515 citations
TL;DR: The framework described in this paper is an attempt to unify adaptive models like artificial neural nets and belief nets for the problem of processing structured information, where relations between data variables are expressed by directed acyclic graphs, where both numerical and categorical values coexist.
Abstract: A structured organization of information is typically required by symbolic processing. On the other hand, most connectionist models assume that data are organized according to relatively poor structures, like arrays or sequences. The framework described in this paper is an attempt to unify adaptive models like artificial neural nets and belief nets for the problem of processing structured information. In particular, relations between data variables are expressed by directed acyclic graphs, where both numerical and categorical values coexist. The general framework proposed in this paper can be regarded as an extension of both recurrent neural networks and hidden Markov models to the case of acyclic graphs. In particular we study the supervised learning problem as the problem of learning transductions from an input structured space to an output structured space, where transductions are assumed to admit a recursive hidden state-space representation. We introduce a graphical formalism for representing this class of adaptive transductions by means of recursive networks, i.e., cyclic graphs where nodes are labeled by variables and edges are labeled by generalized delay elements. This representation makes it possible to incorporate the symbolic and subsymbolic nature of data. Structures are processed by unfolding the recursive network into an acyclic graph called encoding network. In so doing, inference and learning algorithms can be easily inherited from the corresponding algorithms for artificial neural networks or probabilistic graphical model.
508 citations
TL;DR: The M-RAN algorithm is shown to realize networks with far fewer hidden neurons with better or same approximation/classification accuracy and the time taken for learning (training) is also considerably shorter as M- RAN does not require repeated presentation of the training data.
Abstract: Presents a detailed performance analysis of the minimal resource allocation network (M-RAN) learning algorithm, M-RAN is a sequential learning radial basis function neural network which combines the growth criterion of the resource allocating network (RAN) of Platt (1991) with a pruning strategy based on the relative contribution of each hidden unit to the overall network output. The resulting network leads toward a minimal topology for the RAN. The performance of this algorithm is compared with the multilayer feedforward networks (MFNs) trained with 1) a variant of the standard backpropagation algorithm, known as RPROP and 2) the dependence identification (DI) algorithm of Moody and Antsaklis (1996) on several benchmark problems in the function approximation and pattern classification areas. For all these problems, the M-RAN algorithm is shown to realize networks with far fewer hidden neurons with better or same approximation/classification accuracy. Further, the time taken for learning (training) is also considerably shorter as M-RAN does not require repeated presentation of the training data.
462 citations
TL;DR: In this article, three networks are compared for low false alarm stock trend prediction: time delay, recurrent, and probabilistic neural networks (TDNN, RNN, and PNN), utilizing conjugate gradient and multistream extended Kalman filter training for TDNN and RNN.
Abstract: Three networks are compared for low false alarm stock trend predictions. Short-term trends, particularly attractive for neural network analysis, can be used profitably in scenarios such as option trading, but only with significant risk. Therefore, we focus on limiting false alarms, which improves the risk/reward ratio by preventing losses. To predict stock trends, we exploit time delay, recurrent, and probabilistic neural networks (TDNN, RNN, and PNN, respectively), utilizing conjugate gradient and multistream extended Kalman filter training for TDNN and RNN. We also discuss different predictability analysis techniques and perform an analysis of predictability based on a history of daily closing price. Our results indicate that all the networks are feasible, the primary preference being one of convenience.
457 citations
TL;DR: This paper shows that not only is the ADT taxonomy applicable to a cross section of current techniques for extracting rules from trained feedforward ANN's but also how the taxonomy can be adapted and extended to embrace a broader range of ANN types and explanation structures.
Abstract: To date, the preponderance of techniques for eliciting the knowledge embedded in trained artificial neural networks (ANN's) has focused primarily on extracting rule-based explanations from feedforward ANN's. The ADT taxonomy for categorizing such techniques was proposed in 1995 to provide a basis for the systematic comparison of the different approaches. This paper shows that not only is this taxonomy applicable to a cross section of current techniques for extracting rules from trained feedforward ANN's but also how the taxonomy can be adapted and extended to embrace a broader range of ANN types (e,g., recurrent neural networks) and explanation structures. In addition we identify some of the key research questions in extracting the knowledge embedded within ANN's including the need for the formulation of a consistent theoretical basis for what has been, until recently, a disparate collection of empirical results.
421 citations
TL;DR: Proposed is an idea of conditional clustering whose main objective is to develop clusters preserving homogeneity of the clustered patterns with regard to their similarity in the input space as well as their respective values assumed in the output space.
Abstract: This paper is concerned with the use of radial basis function (RBF) neural networks aimed at an approximation of nonlinear mappings from R/sup n/ to R. The study is devoted to the design of these networks, especially their layer composed of RBF, using the techniques of fuzzy clustering. Proposed is an idea of conditional clustering whose main objective is to develop clusters (receptive fields) preserving homogeneity of the clustered patterns with regard to their similarity in the input space as well as their respective values assumed in the output space. The detailed clustering algorithm is accompanied by extensive simulation studies.
389 citations
TL;DR: The computing and storage capabilities of morphological associative memories are examined and differences between morphological models and traditional semilinear models such as the Hopfield net are discussed.
Abstract: The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. A nonlinear activation function usually follows the linear operation in order to provide for nonlinearity of the network and set the next state of the neuron. In this paper we introduce a novel class of artificial neural networks, called morphological neural networks, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before possible application of a nonlinear activation function. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. The main emphasis of the research presented here is on morphological associative memories. We examine the computing and storage capabilities of morphological associative memories and discuss differences between morphological models and traditional semilinear models such as the Hopfield net.
369 citations
TL;DR: A sufficient condition related to the existence of unique equilibrium point and its robust stability is derived and a novel interval dynamic Hopfield neural network (IDHNN) model is derived.
Abstract: The conventional Hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic Hopfield neural network (IDHNN) model. A sufficient condition related to the existence of unique equilibrium point and its robust stability is derived.
TL;DR: It is shown that the control signals obtained can also make the real system output close to the set point, and the applicability of the proposed method is demonstrated.
Abstract: In this paper a direct adaptive neural-network control strategy for unknown nonlinear systems is presented. The system considered is described by an unknown NARMA model, and a feedforward neural network is used to learn the system. Taking the neural network as a neural model of the system, control signals are directly obtained by minimizing either the instant difference or the cumulative differences between a set point and the output of the neural model. Since the training algorithm guarantees that the output of the neural model approaches that of the actual system, it is shown that the control signals obtained can also make the real system output close to the set point. An application to a flow-rate control system is included to demonstrate the applicability of the proposed method and desired results are obtained.
TL;DR: It is proved that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets, in contrast with the gradient methods whose convergence is not guaranteed.
Abstract: We present a general methodology for designing optimization neural networks. We prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets, in contrast with the gradient methods whose convergence is not guaranteed. We show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases. Based on the theoretical results of the proposed method, we study the convergence and stability of general gradient models in the case of unisolated solutions. Using the proposed method, we derive some new neural network models for a very large class of optimization problems, in which the equilibrium points correspond to exact solutions and there is no variable parameter. Finally, some numerical examples show the effectiveness of the method.
TL;DR: A linguistic (qualitative) modeling approach which combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GA's) in a fuzzy-neural network (FNN) form which can handle both quantitative and qualitative knowledge.
Abstract: Linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems, and fuzzy logic represents one of the most effective algorithms to build such linguistic models. In this paper, a linguistic (qualitative) modeling approach is proposed. The approach combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GAs). The proposed model is presented in a fuzzy-neural network (FNN) form which can handle both quantitative (numerical) and qualitative (linguistic) knowledge. The learning algorithm of a FNN is composed of three phases. The first phase is used to find the initial membership functions of the fuzzy model. In the second phase, a new algorithm is developed and used to extract the linguistic-fuzzy rules. In the third phase, a multiresolutional dynamic genetic algorithm (MRD-GA) is proposed and used for optimized tuning of membership functions of the proposed model. Two well-known benchmarks are used to evaluate the performance of the proposed modeling approach, and compare it with other modeling approaches.
TL;DR: In this collection of interviews, those who helped to shape the field share their childhood memories, their influences, how they became interested in neural networks, and what they see as its future.
Abstract: Since World War II, a group of scientists has been attempting to understand the human nervous system and to build computer systems that emulate the brain's abilities. Many of the early workers in this field of neural networks came from cybernetics; others came from neuroscience, physics, electrical engineering, mathematics, psychology, even economics. In this collection of interviews, those who helped to shape the field share their childhood memories, their influences, how they became interested in neural networks, and what they see as its future. The subjects tell stories that have been told, referred to, whispered about, and imagined throughout the history of the field. Together, the interviews form a Rashomon-like web of reality. Some of the mythic people responsible for the foundations of modern brain theory and cybernetics, such as Norbert Wiener, Warren McCulloch, and Frank Rosenblatt, appear prominently in the recollections. The interviewees agree about some things and disagree about more. Together, they tell the story of how science is actually done, including the false starts, and the Darwinian struggle for jobs, resources, and reputation. Although some of the interviews contain technical material, there is no actual mathematics in the book. Contributors: James A. Anderson, Michael Arbib, Gail Carpenter, Leon Cooper, Jack Cowan, Walter Freeman, Stephen Grossberg, Robert Hecht-Neilsen, Geoffrey Hinton, Teuvo Kohonen, Bart Kosko, Jerome Lettvin, Carver Mead, David Rumelhart, Terry Sejnowski, Paul Werbos, Bernard Widrow.
TL;DR: A new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function is suggested by gradually reducing the time step in the Euler approximation of the differential equations that describe the continuous Hopfield neural network.
Abstract: Chen and Aihara (1995) proposed a chaotic simulated annealing approach to solving optimization problems. By adding a negative self coupling to a network model proposed earlier by Aihara et al. and gradually removing this negative self-coupling, they used the transient chaos for searching and self-organizing, thereby achieving great improvement over other neural-network approaches to optimization problems with or without simulated annealing. In this paper we suggest a new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function by gradually reducing the time step in the Euler approximation of the differential equations that describe the continuous Hopfield neural network. This approach eliminates the need to carefully select other system parameters. We also generalize the convergence theorems of Chen and Aihara to arbitrarily increasing neuronal input-output functions and to less restrictive and yet more compact forms.
TL;DR: Using this scheme, not only strong robustness with respect to uncertain dynamics and nonlinearities can be obtained, but also the output tracking error between the plant output and the desired reference output can asymptotically converge to zero.
Abstract: A neural-network-based adaptive tracking control scheme is proposed for a class of nonlinear systems in this paper. It is shown that RBF neural networks are used to adaptively learn system uncertainty bounds in the Lyapunov sense, and the outputs of the neural networks are then used as the parameters of the controller to compensate for the effects of system uncertainties. Using this scheme, not only strong robustness with respect to uncertain dynamics and nonlinearities can be obtained, but also the output tracking error between the plant output and the desired reference output can asymptotically converge to zero. A simulation example is performed in support of the proposed neural control scheme.
TL;DR: This paper describes how the SGOCE paradigm has been used to evolve developmental programs capable of generating recurrent neural networks that control the behavior of simulated insects.
Abstract: This paper describes how the SGOCE paradigm has been used to evolve developmental programs capable of generating recurrent neural networks that control the behavior of simulated insects. This paradigm is characterized by an encoding scheme, an evolutionary algorithm, syntactic constraints, and an incremental strategy that are described in turn. The additional use of an insect model equipped with six legs and two antennae made it possible to generate control modules that allowed it to successively add gradient-following and obstacle-avoidance capacities to walking behavior. The advantages of this evolutionary approach, together with directions for future work, are discussed.
TL;DR: A neural-network version of an H(infinity)-based identification algorithm from Didinsky et al is presented and it is shown how this algorithm leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the system nonlinearity.
Abstract: We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. (1995). We present a class of identifiers which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. Subsequently, we address the same problem under a third, worst case L/sup /spl infin// criterion for an RBF modeling. We present a neural-network version of an H/sup /spl infin//-based identification algorithm from Didinsky et al., and show how it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity.
TL;DR: A new adaptive fuzzy reasoning method using compensatory fuzzy operators is proposed to make a fuzzy logic system more adaptive and more effective and is proved to be a universal approximator.
Abstract: In this paper, a new adaptive fuzzy reasoning method using compensatory fuzzy operators is proposed to make a fuzzy logic system more adaptive and more effective. Such a compensatory fuzzy logic system is proved to be a universal approximator. The compensatory neural fuzzy networks built by both control-oriented fuzzy neurons and decision-oriented fuzzy neurons cannot only adaptively adjust fuzzy membership functions but also dynamically optimize the adaptive fuzzy reasoning by using a compensatory learning algorithm. The simulation results of a cart-pole balancing system and nonlinear system modeling have shown that: 1) the compensatory neurofuzzy system can effectively learn commonly used fuzzy IF-THEN rules from either well-defined initial data or ill-defined data; 2) the convergence speed of the compensatory learning algorithm is faster than that of the conventional backpropagation algorithm; and 3) the efficiency of the compensatory learning algorithm can be improved by choosing an appropriate compensatory degree.
TL;DR: This paper presents a compression scheme for digital still images, by using the Kohonen's neural network algorithm, not only for its vector quantization feature, but also for its topological property, which allows an increase of about 80% for the compression rate.
Abstract: Presents a compression scheme for digital still images, by using Kohonen's neural network algorithm, not only for its vector quantization feature, but also for its topological property. This property allows an increase of about 80% for the compression rate. Compared to the JPEG standard, this compression scheme shows better performances (in terms of PSNR) for compression rates higher than 30.
TL;DR: A new scheme of knowledge encoding in a fuzzy multilayer perceptron (MLP) using rough set-theoretic concepts is described, demonstrating the superiority of the system over the fuzzy and conventional versions of the MLP (involving no initial knowledge).
Abstract: A scheme of knowledge encoding in a fuzzy multilayer perceptron (MLP) using rough set-theoretic concepts is described. Crude domain knowledge is extracted from the data set in the form of rules. The syntax of these rules automatically determines the appropriate number of hidden nodes while the dependency factors are used in the initial weight encoding. The network is then refined during training. Results on classification of speech and synthetic data demonstrate the superiority of the system over the fuzzy and conventional versions of the MLP (involving no initial knowledge).
TL;DR: The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine, particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.
Abstract: This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.
TL;DR: A robust neural-network (NN) controller is proposed for the motion control of rigid-link electrically driven (RLED) robots that can be regarded as a universal reusable controller because the same controller can be applied to any type of RLED robots without any modifications.
Abstract: A robust neural-network (NN) controller is proposed for the motion control of rigid-link electrically driven (RLED) robots. Two-layer NN's are used to approximate two very complicated nonlinear functions. The main advantage of our approach is that the NN weights are tuned online, with no off-line learning phase required. Most importantly, we can guarantee the uniformly ultimately bounded (UUB) stability of tracking errors and NN weights. When compared with standard adaptive robot controllers, we do not require lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of RLED robots without any modifications.
TL;DR: A neural-network-based control design for a discrete-time nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin and the stability of the closed-loop is guaranteed.
Abstract: We address a neural network-based control design for a discrete-time nonlinear system. Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin. A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a state feedback control law for the nonlinear system based on the certainty equivalence principle. The control design equations are shown to be a set of linear matrix inequalities where a convex optimization algorithm can be applied to determine the control signal. Further, the stability of the closed-loop is guaranteed in the sense that there exists a unique global attraction region in the neighborhood of the origin to which every trajectory of the closed-loop system converges. Finally, a simple example is presented so as to illustrate our control design procedure.
TL;DR: A geometric interpretation for Kramer's nonlinear principal components analysis (NLPCA) method is proposed by showing that NLPCA fits a lower-dimensional curve or surface through the training data.
Abstract: Kramer's (1991) nonlinear principal components analysis (NLPCA) neural networks are feedforward autoassociative networks with five layers. The third layer has fewer nodes than the input or output layers. This paper proposes a geometric interpretation for Kramer's method by showing that NLPCA fits a lower-dimensional curve or surface through the training data. The first three layers project observations onto the curve or surface giving scores. The last three layers define the curve or surface. The first three layers are a continuous function, which we show has several implications: NLPCA "projections" are suboptimal producing larger approximation error, NLPCA is unable to model curves and surfaces that intersect themselves, and NLPCA cannot parameterize curves with parameterizations having discontinuous jumps. We establish results on the identification of score values and discuss their implications on interpreting score values. We discuss the relationship between NLPCA and principal curves and surfaces, another nonlinear feature extraction method.
TL;DR: A Hopfield network which enables feasibility of the solutions to be ensured and improved solution quality through escape from local minima, and a self-organizing neural network which generalizes to solve a broad class of combinatorial optimization problems are proposed.
Abstract: After more than a decade of research, there now exist several neural-network techniques for solving NP-hard combinatorial optimization problems. Hopfield networks and self-organizing maps are the two main categories into which most of the approaches can be divided. Criticism of these approaches includes the tendency of the Hopfield network to produce infeasible solutions, and the lack of generalizability of the self-organizing approaches (being only applicable to Euclidean problems). The paper proposes two new techniques which have overcome these pitfalls: a Hopfield network which enables feasibility of the solutions to be ensured and improved solution quality through escape from local minima, and a self-organizing neural network which generalizes to solve a broad class of combinatorial optimization problems. Two sample practical optimization problems from Australian industry are then used to test the performances of the neural techniques against more traditional heuristic solutions.
TL;DR: A method based on three neural networks of the local linear map type which enables a computer to identify the head orientation of a user by learning from examples is presented.
Abstract: Humans easily recognize where another person is looking and often use this information for interspeaker coordination. We present a method based on three neural networks of the local linear map type which enables a computer to identify the head orientation of a user by learning from examples. One network is used for color segmentation, a second for localization of the face, and the third for the final recognition of the head orientation. The system works at a frame rate of one image per second on a common workstation, We analyze the accuracy achieved at different processing steps and discuss the usability of the approach in the context of a visual human-machine interface.
TL;DR: The analysis shows that as long as a reduced dimension subvector of the regressor vector is PE, then a specialized form of exponential convergence will be achieved, which is critical since the general PE conditions are not practical in most control applications.
Abstract: This paper investigates nonparametric nonlinear adaptive control under passive learning conditions. Passive learning refers to the normal situation in control applications in which the system inputs cannot be selected freely by the learning system. This article also analyzes the stability of both the system state and approximator parameter estimates. Stability results are presented for both parametric (known model structure with unknown parameters) and nonparametric (unknown model structure resulting in /spl epsiv/-approximation error) adaptive control applications. Upper bounds on the tracking error are developed. The article also analyzes the persistence (PE) of excitation conditions required for parameter convergence. In addition, to a general PE analysis, the article presents a specific analysis pertinent to approximators that are composed of basis elements with local support. In particular, the analysis shows that as long as a reduced dimension subvector of the regressor vector is PE, then a specialized form of exponential convergence will be achieved. This condition is critical, since the general PE conditions are not practical in most control applications. In addition to the PE results, this article explicitly defines the regions over which the approximator converges when locally supported basis elements are used. The results are demonstrated throughout via examples.
TL;DR: This paper addresses issues by initializing RBF networks with decision trees that define relatively pure regions in the instance space; each of these regions then determines one basis function.
Abstract: Successful implementations of radial-basis function (RBF) networks for classification tasks must deal with architectural issues, the burden of irrelevant attributes, scaling, and some other problems. This paper addresses these issues by initializing RBF networks with decision trees that define relatively pure regions in the instance space; each of these regions then determines one basis function. The resulting network is compact, easy to induce, and has favorable classification accuracy.