SEARCH · PubMed Health

Results for “radial basis function network”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources

PubMed1995

Predicting free energy contributions to the conformational stability of folded proteins from the residue sequence with radial basis function networks.

Radial basis function neural networks are trained on a data base comprising 38 globular proteins of well resolved crystallographic structure and the corresponding free energy contributions to the overall protein stability (as computed partially from chrystallographic analysis and partially with multiple regression from experimental thermodynamic data by Ponnuswamy and Gromiha (1994)). Starting from the residue sequence and using as input code the percentage of each residue and the total residue number of the protein, it is found with a cross-validation method that neural networks can optimally predict the free energy contributions due to hydrogen bonds, hydrophobic interactions and the unfolded state. Terms due to electrostatic and disulfide bonding free energies are poorly predicted. This is so also when other input codes, including the percentage of secondary structure type of the protein and/or residue-pair information are used. Furthermore, trained on the computed and/or experimental delta G values of the data base, neural networks predict a conformational stability ranging from about 10 to 20 kcal mol-1 rather independently of the residue sequence, with an average error per protein of about 9 kcal mol-1.

Calorimetry↗

PubMed2000

Radical pruning: a method to construct skeleton radial basis function networks.

Trained radial basis function networks are well-suited for use in extracting rules and explanations because they contain a set of locally tuned units. However, for rule extraction to be useful, these networks must first be pruned to eliminate unnecessary weights. The pruning algorithm cannot search the network exhaustively because of the computational effort involved. It is shown that using multiple pruning methods with smart ordering of the pruning candidates, the number of weights in a radial basis function network can be reduced to a small fraction of the original number. The complexity of the pruning algorithm is quadratic (instead of exponential) in the number of network weights. Pruning performance is shown using a variety of benchmark problems from the University of California, Irvine machine learning database.

Algorithms↗

PubMed2005

Sensitivity analysis applied to the construction of radial basis function networks.

Conventionally, a radial basis function (RBF) network is constructed by obtaining cluster centers of basis function by maximum likelihood learning. This paper proposes a novel learning algorithm for the construction of radial basis function using sensitivity analysis. In training, the number of hidden neurons and the centers of their radial basis functions are determined by the maximization of the output's sensitivity to the training data. In classification, the minimal number of such hidden neurons with the maximal sensitivity will be the most generalizable to unknown data. Our experimental results show that our proposed sensitivity-based RBF classifier outperforms the conventional RBFs and is as accurate as support vector machine (SVM). Hence, sensitivity analysis is expected to be a new alternative way to the construction of RBF networks.

Algorithms↗

PubMed2006

Quantitative structure-toxicity relationships (QSTRs): a comparative study of various non linear methods. General regression neural network, radial basis function neural network and support vector machine in predicting toxicity of nitro- and cyano- aromatics to Tetrahymena pyriformis.

Prediction of toxicity of 203 nitro- and cyano-aromatic chemicals to Tetrahymena pyriformis was carried out by radial basis function neural network, general regression neural network and support vector machine, in non-linear response surface methodology. Toxicity was predicted from hydrophobicity parameter (log Kow) and maximum superdelocalizability (Amax). Special attention was drawn to prediction ability and robustness of the models, investigated both in a leave-one-out and 10-fold cross validation (CV) processes. The influence that the corresponding changes in the learning sets during these CV processes could have on a common external test set including 41 compounds was also examined. This allowed us to establish the stability of the models. The non linear results slightly outperform (as expected) multilinear relationships (MLR) and also favourably compete with various other non linear approaches recently proposed by Ren (J. Chem. Inf. Comput. Sci., 43 1679 (2003)).

Animals↗

PubMed1995

Learning and generalization in radial basis function networks.

The two-layer radial basis function network, with fixed centers of the basis functions, is analyzed within a stochastic training paradigm. Various definitions of generalization error are considered, and two such definitions are employed in deriving generic learning curves and generalization properties, both with and without a weight decay term. The generalization error is shown analytically to be related to the evidence and, via the evidence, to the prediction error and free energy. The generalization behavior is explored; the generic learning curve is found to be inversely proportional to the number of training pairs presented. Optimization of training is considered by minimizing the generalization error with respect to the free parameters of the training algorithms. Finally, the effect of the joint activations between hidden-layer units is examined and shown to speed training.

Artificial Intelligence↗

PubMed1998

Estimation of spatiotemporal neural activity using radial basis function networks.

We report a method using radial basis function (RBF) networks to estimate the time evolution of population activity in topologically organized neural structures from single-neuron recordings. This is an important problem in neuroscience research, as such estimates may provide insights into systems-level function of these structures. Since single-unit neural data tends to be unevenly sampled and highly variable under similar behavioral conditions, obtaining such estimates is a difficult task. In particular, a class of cells in the superior colliculus called buildup neurons can have very narrow regions of saccade vectors for which they discharge at high rates but very large surround regions over which they discharge at low, but not zero, levels. Estimating the dynamic movement fields for these cells for two spatial dimensions at closely spaced timed intervals is a difficult problem, and no general method has been described that can be applied to all buildup cells. Estimation of individual collicular cells' spatiotemporal movement fields is a prerequisite for obtaining reliable two-dimensional estimates of the population activity on the collicular motor map during saccades. Therefore, we have developed several computational-geometry-based algorithms that regularize the data before computing a surface estimation using RBF networks. The method is then expanded to the problem of estimating simultaneous spatiotemporal activity occurring across the superior colliculus during a single movement (the inverse problem). In principle, this methodology could be applied to any neural structure with a regular, two-dimensional organization, provided a sufficient spatial distribution of sampled neurons is available.

Algorithms↗

PubMed2004

Multiscale approximation with hierarchical radial basis functions networks.

An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-D) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.

Face↗

PubMed2001

Three learning phases for radial-basis-function networks.

In this paper, learning algorithms for radial basis function (RBF) networks are discussed. Whereas multilayer perceptrons (MLP) are typically trained with backpropagation algorithms, starting the training procedure with a random initialization of the MLP's parameters, an RBF network may be trained in many different ways. We categorize these RBF training methods into one-, two-, and three-phase learning schemes. Two-phase RBF learning is a very common learning scheme. The two layers of an RBF network are learnt separately; first the RBF layer is trained, including the adaptation of centers and scaling parameters, and then the weights of the output layer are adapted. RBF centers may be trained by clustering, vector quantization and classification tree algorithms, and the output layer by supervised learning (through gradient descent or pseudo inverse solution). Results from numerical experiments of RBF classifiers trained by two-phase learning are presented in three completely different pattern recognition applications: (a) the classification of 3D visual objects; (b) the recognition hand-written digits (2D objects); and (c) the categorization of high-resolution electrocardiograms given as a time series (ID objects) and as a set of features extracted from these time series. In these applications, it can be observed that the performance of RBF classifiers trained with two-phase learning can be improved through a third backpropagation-like training phase of the RBF network, adapting the whole set of parameters (RBF centers, scaling parameters, and output layer weights) simultaneously. This, we call three-phase learning in RBF networks. A practical advantage of two- and three-phase learning in RBF networks is the possibility to use unlabeled training data for the first training phase. Support vector (SV) learning in RBF networks is a different learning approach. SV learning can be considered, in this context of learning, as a special type of one-phase learning, where only the output layer weights of the RBF network are calculated, and the RBF centers are restricted to be a subset of the training data. Numerical experiments with several classifier schemes including k-nearest-neighbor, learning vector quantization and RBF classifiers trained through two-phase, three-phase and support vector learning are given. The performance of the RBF classifiers trained through SV learning and three-phase learning are superior to the results of two-phase learning, but SV learning often leads to complex network structures, since the number of support vectors is not a small fraction of the total number of data points.

Algorithms↗

PubMed1996

Radial Basis Function Networks: Generalization in Over-realizable and Unrealizable Scenarios.

Learning and generalization in a two-layer radial basis function network, with fixed centres of the basis functions, is examined within a stochastic training paradigm. Employing a Bayesian approach, expressions for generalization error are derived under the assumption that the generating mechanism (teacher) for the training data is also a radial basis function network, but one for which the basis function centres and widths need not correspond to those of the student network. The effects of regularization, via a weight decay term, are examined. The cases in which the student has greater representational power than the teacher (over-realizable), and in which the teacher has greater power than the student (unrealizable) are studied. Dependence on knowing the centres of the teacher is eliminated by introducing a single degree-of-confidence parameter. Finally, simulations are performed which validate the analytic results. Copyright 1996 Elsevier Science Ltd.

Journal Article↗

PubMed2001

Numerical solution of differential equations using multiquadric radial basis functions networks.

This paper presents mesh-free procedures for solving linear differential equations (ODEs and elliptic PDEs) based on multiquadric (MQ) radial basis function networks (RBFNs). Based on our study of approximation of function and its derivatives using RBFNs that was reported in an earlier paper (Mai-Duy, N. & Tran-Cong, T. (1999). Approximation of function and its derivatives using radial basis function networks. Neural networks, submitted), new RBFN approximation procedures are developed in this paper for solving DEs, which can also be classified into two types: a direct (DRBFN) and an indirect (IRBFN) RBFN procedure. In the present procedures, the width of the RBFs is the only adjustable parameter according to a(i) = betad(i), where d(i) is the distance from the ith centre to the nearest centre. The IRBFN method is more accurate than the DRBFN one and experience so far shows that beta can be chosen in the range 7 < or = beta 10 for the former. Different combinations of RBF centres and collocation points (uniformly and randomly distributed) are tested on both regularly and irregularly shaped domains. The results for a 1D Poisson's equation show that the DRBFN and the IRBFN procedures achieve a norm of error of at least O(1.0 x 10(-4)) and O(1.0 x 10(-8)), respectively, with a centre density of 50. Similarly, the results for a 2D Poisson's equation show that the DRBFN and the IRBFN procedures achieve a norm of error of at least O(1.0 x 10(-3)) and O(1.0 x10(-6)) respectively, with a centre density of 12 X 12.

Models, Biological↗

PubMed1998

Dual-orthogonal radial basis function networks for nonlinear time series prediction.

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

Journal Article↗

PubMed2000

Combining regression trees and radial basis function networks.

We describe a method for non-parametric regression which combines regression trees with radial basis function networks. The method is similar to that of Kubat, who was first to suggest such a combination, but has some significant improvements. We demonstrate the features of the new method, compare its performance with other methods on DELVE data sets and apply it to a real world problem involving the classification of soybean plants from digital images.

Models, Statistical↗

PubMed2003

Relaxed conditions for radial-basis function networks to be universal approximators.

In this paper, we investigate the universal approximation property of Radial Basis Function (RBF) networks. We show that RBFs are not required to be integrable for the REF networks to be universal approximators. Instead, RBF networks can uniformly approximate any continuous function on a compact set provided that the radial basis activation function is continuous almost everywhere, locally essentially bounded, and not a polynomial. The approximation in L(p)(micro)(1 < or = p < infinity) space is also discussed. Some experimental results are reported to illustrate our findings.

Neural Networks, Computer↗

PubMedDate not supplied

Adaptive configuring of radial basis function network by hybrid particle swarm algorithm for QSAR studies of organic compounds.

The configuring of a radial basis function network (RBFN) consists of selecting the network parameters (centers and widths in RBF units and weights between the hidden and output layers) and network architecture. The issues of suboptimum and overfitting, however, often occur in RBFN configuring. This paper presented a hybrid particle swarm optimization (HPSO) algorithm to simultaneously search the optimal network structure and parameters involved in the RBFN (HPSORBFN) with an ellipsoidal Gaussian function as a basis function. The continuous version of PSO was used for parameter training, while the modified discrete PSO was employed to determine the appropriate network topology. The proposed HPSORBFN algorithm was applied to modeling the inhibitory activities of substituted bis[(acridine-4-carboxamide)propyl]methylamines to murine P388 leukemia cells and the bioactivities of COX-2 inhibitors. The results were compared with those obtained from RBFNs with the parameters optimized by continuous PSO and by conventionally RBFN training the algorithm for a fixed network topology, indicating that the HPSO was competent for RBFN configuring in that it converged quickly toward the optimal solution and avoided overfitting.

Algorithms↗

PubMed1998

Mouse chromosome classification by radial basis function network with fast orthogonal search.

This paper provides the results of our study on automatic classification of mouse chromosomes. A radial basis function neural network was compared with a multi-layer perceptron and a probabilistic neural network. The networks were trained and tested with 3723 chromosomes presented to each network as 30-point banding profiles. The radial basis function classifier trained with the fast orthogonal search learning rule provided the best unconstrained classification error rate of 12.7% which was obtained with a training set of 2250 chromosomes.

Journal Article↗

PubMed2005

[Radial basis function networks and IR spectrometry applied for identification of official rhubarb samples].

The Fourier transform infrared spectrometry (FTIRS) and radial basis function neural network (RBF-NN) have been applied to develop classification models for identifying official and unofficial rhubarb samples. The original data were compressed from 775 variables to 49 variables by using wavelet transformation method. The compressed spectra with reduced variables maintain the characteristics of the IR spectra and speed up the network training process. The effects of network parameters including error goal and spread constant, were investigated. The rate of correct classification is up to 97.78% at optimized conditions. Results show that the combination of IRS and ANN can be used as fast and convenient tool for identification of Chinese herbal samples.

Algorithms↗

PubMed2005

Smart chemical taste sensor for determination and prediction of taste qualities based on a two-phase optimized radial basis function network.

A novel, smart, chemical taste sensor that realistically mimics the behavior of the human gustatory system is described. The taste sensor consists of an array of electrochemical sensors that represent the gustatory receptors on the human tongue, and a two-phase optimized radial basis function network (RBFN) to represent the human brain, which comprehensively analyzes the gustatory stimulation and judges the overall taste. In the illustrated model, eight electrodes were fabricated to determine the eight major taste-causing substances, Na+, K+, Cl-, H+, sucrose, glucose, glutamate, and caffeine. The detected signals were fed to a two-phase RBFN optimized by the implementation of a basis optimization algorithm and weight decay term for appropriate data processing. The first phase of the two-phase RBFN quantifies the amount of taste-causing substances in food samples from the responses of the electrodes. These results are then fed to the second phase, which correlates the amount of substances with the overall taste. The final output is scored on a scale of 1-5 for each of the five basic tastes sensed by the human gustatory system, which are saltiness, sourness, sweetness, bitterness, and umami. The constructed network estimated the intensity of the basic tastes of 30 drink varieties with an average relative error of 7.0% compared to the human scores. The network could also estimate the variance in the human sensory perception. Moreover, the sensor successfully predicted the interactions of tastes such as suppression of bitterness by sweetness and enhancement of umami by saltiness, which are illusions sensed by the human gustatory system. With these abilities, the novel taste sensor can be considered as a quantitative yet humanlike sensor with a great potential for practical applications.

Algorithms↗

PubMed2006

Real-time data-reusing adaptive learning of a radial basis function network for tracking evoked potentials.

Tracking variations in both the latency and amplitude of evoked potential (EP) is important in quantifying properties of the nervous system. Adaptive filtering is a powerful tool for tracking such variations. In this paper, a data-reusing non-linear adaptive filtering method, based on a radial basis function network (RBFN), is implemented to estimate EP. The RBFN consists of an input layer of source nodes, a single hidden layer of non-linear processing units and an output layer of linear weights. It has built-in nonlinear activation functions that allow learning of function mappings. Moreover, it produces satisfactory estimates of signals against a background noise without a priori knowledge of the signal, provided that the signal and noise are independent. In clinical situations where EP responses change rapidly, the convergence rate of the algorithm becomes a critical factor. A carefully designed data-reusing RBFN can accelerate the convergence rate markedly and, thus, enhance its performance. Both theoretical analysis and simulation results support the improved performance of our new algorithm.

Adolescent↗