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Results for “radial basis function network”

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PubMed2002

Descartes' rule of signs for radial basis function neural networks.

We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the Vapnik-Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two or more input nodes have superlinear VC dimension. The rules also give rise to lower bounds for network sizes, thus demonstrating the relevance of network parameters for the complexity of computing with RBF neural networks.

Journal Article↗

PubMed2005

Radial basis function neural networks in non-destructive determination of compound aspirin tablets on NIR spectroscopy.

The application of the second most popular artificial neural networks (ANNs), namely, the radial basis function (RBF) networks, has been developed for quantitative analysis of drugs during the last decade. In this paper, the two components (aspirin and phenacetin) were simultaneously determined in compound aspirin tablets by using near-infrared (NIR) spectroscopy and RBF networks. The total database was randomly divided into a training set (50) and a testing set (17). Different preprocessing methods (standard normal variate (SNV), multiplicative scatter correction (MSC), first-derivative and second-derivative) were applied to two sets of NIR spectra of compound aspirin tablets with different concentrations of two active components and compared each other. After that, the performance of RBF learning algorithm adopted the nearest neighbor clustering algorithm (NNCA) and the criterion for selection used a cross-validation technique. Results show that using RBF networks to quantificationally analyze tablets is reliable, and the best RBF model was obtained by first-derivative spectra.

Aspirin↗

PubMed2006

A fast identification algorithm for Box-Cox transformation based radial basis function neural network.

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

Algorithms↗

PubMed2005

Blind equalization using a predictive radial basis function neural network.

In this paper, we propose a novel blind equalization approach based on radial basis function (RBF) neural networks. By exploiting the short-term predictability of the system input, a RBF neural net is used to predict the inverse filter output. It is shown here that when the prediction error of the RBF neural net is minimized, the coefficients of the inverse system are identical to those of the unknown system. To enhance the identification performance in noisy environments, the improved least square (ILS) method based on the concept of orthogonal distance to red the estimation bias caused by additive measurement noise is proposed here to perform the training. The convergence rate of the ILS learning is analyzed, and the asymptotic mean square error (MSE) of the proposed predictive RBF identification method is derived theoretically. Monte Carlo simulations show that the proposed method is effective for blind system identification. The new blind technique is then applied to two practical applications: equalization of real-life radar sea clutter collected at the east coast of Canada and deconvolution of real speech signals. In both cases, the proposed blind equalization technique is found to perform satisfactory even when the channel effects and measurement noise are strong.

Algorithms↗

PubMed2001

Comparison of statistical methods for identification of Streptococcus thermophilus, Enterococcus faecalis, and Enterococcus faecium from randomly amplified polymorphic DNA patterns.

Thermophilic streptococci play an important role in the manufacture of many European cheeses, and a rapid and reliable method for their identification is needed. Randomly amplified polymorphic DNA (RAPD) PCR (RAPD-PCR) with two different primers coupled to hierarchical cluster analysis has proven to be a powerful tool for the classification and typing of Streptococcus thermophilus, Enterococcus faecium, and Enterococcus faecalis (G. Moschetti, G. Blaiotta, M. Aponte, P. Catzeddu, F. Villani, P. Deiana, and S. Coppola, J. Appl. Microbiol. 85:25-36, 1998). In order to develop a fast and inexpensive method for the identification of thermophilic streptococci, RAPD-PCR patterns were generated with a single primer (XD9), and the results were analyzed using artificial neural networks (Multilayer Perceptron, Radial Basis Function network, and Bayesian network) and multivariate statistical techniques (cluster analysis, linear discriminant analysis, and classification trees). Cluster analysis allowed the identification of S. thermophilus but not of enterococci. A Bayesian network proved to be more effective than a Multilayer Perceptron or a Radial Basis Function network for the identification of S. thermophilus, E. faecium, and E. faecalis using simplified RAPD-PCR patterns (obtained by summing the bands in selected areas of the patterns). The Bayesian network also significantly outperformed two multivariate statistical techniques (linear discriminant analysis and classification trees) and proved to be less sensitive to the size of the training set and more robust in the response to patterns belonging to unknown species.

Bayes Theorem↗

PubMed2001

Radial basis function neural network approach for the diagnosis of coronary artery disease based on the standard electrocardiogram exercise test.

The purpose of the paper is the evaluation of a radial basis function neural network as a tool for computer aided coronary artery disease diagnosis based on the results of the traditional ECG exercise test. The research was performed using 776 data records from an exercise test (297 records from healthy patients and 479 from ill patients) confirmed by coronary arteriography results. Each record described the state of the patient, provided input data for the neural network, included the level and slope of an ST segment of a 12-lead ECG signal made at rest and after effort, heart rate, blood pressure, load during the test, and occurrence of coronary pain, coronary arteriography, correct output pattern for the neural network, and verified the existence (or not) of more than 50% stenosis of the particular coronary vessels. Radial basis function neural networks for coronary artery disease diagnosis were optimised by choosing the type of radial function, the method of training (setting the number of centres and their dimensions), and regularisation. The best network correctly recognised over 97% of cases from a 400-element test set, diagnosing not only the patients' condition (simple 'healthy/unhealthy' diagnosis), but also pointing out individual unhealthy/stenosed vessels.

Adult↗

PubMedDate not supplied

An efficient learning algorithm for improving generalization performance of radial basis function neural networks.

This paper presents an efficient recursive learning algorithm for improving generalization performance of radial basis function (RBF) neural networks. The approach combines the rival penalized competitive learning (PRCL) [Xu, L., Kizyzak, A. & Oja, E. (1993). Rival penalized competitive learning for clustering analysis, RBF net and curve detection, IEEE Transactions on Neural Networks, 4, 636-649] and the regularized least squares (RLS) to provide an efficient and powerful procedure for constructing a minimal RBF network that generalizes very well. The RPCL selects the number of hidden units of network and adjusts centers, while the RLS constructs the parsimonious network and estimates the connection weights. In the RLS we derived a simple recursive algorithm, which needs no matrix calculation, and so largely reduces the computational cost. This combined algorithm significantly enhances the generalization performance and the real-time capability of the RBF networks. Simulation results of three different problems demonstrate much better generalization performance of the present algorithm over other existing similar algorithms.

Algorithms↗

PubMed2001

Modelling and prediction for chaotic fir laser attractor using rational function neural network.

Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability.

Infrared Rays↗

PubMed2006

Training reformulated radial basis function neural networks capable of identifying uncertainty in data classification.

This paper introduces a learning algorithm that can be used for training reformulated radial basis function neural networks (RBFNNs) capable of identifying uncertainty in data classification. This learning algorithm trains a special class of reformulated RBFNNs, known as cosine RBFNNs, by updating selected adjustable parameters to minimize the class-conditional variances at the outputs of their radial basis functions (RBFs). The experiments verify that quantum neural networks (QNNs) and cosine RBFNNs trained by the proposed learning algorithm are capable of identifying uncertainty in data classification, a property that is not shared by cosine RBFNNs trained by the original learning algorithm and conventional feed-forward neural networks (FFNNs). Finally, this study leads to a simple classification strategy that can be used to improve the classification accuracy of QNNs and cosine RBFNNs by rejecting ambiguous feature vectors based on their responses.

Algorithms↗

PubMedDate not supplied

Radial basis function neural networks for nonlinear Fisher discrimination and Neyman-Pearson classification.

We propose a novel technique for the design of radial basis function (RBF) neural networks (NNs). To select various RBF parameters, the class membership information of training samples is utilized to produce new cluster classes. This allows emphasis of classification performance for certain class data rather than best overall classification. This allows us to control performance as desired and to approximate Neyman-Pearson classification. We also show that by properly choosing the desired output neuron levels, then the RBF hidden to output layer performs Fisher discrimination analysis, and that the full system performs a nonlinear Fisher analysis. Data on an agricultural product inspection problem and on synthetic data confirm the effectiveness of these methods.

Animals↗

PubMed2001

A short-term temperature forecaster based on a novel radial basis functions neural network.

Many applications dealing with electric load forecasting in buildings require temperature prediction. A new method for short-term temperature forecasting based on a Radial Basis Functions Neural Network, initialized by a Regression Tree, is presented. In this method, each terminal node of the tree contributes one hidden unit to the RBF network. The forecaster uses the current coded hour and the temperature as inputs, and predicts the next hour temperature. The results demonstrate this predictor can be used for load forecasting.

Neural Networks, Computer↗

PubMedDate not supplied

Quantitative prediction of liquid chromatography retention of N-benzylideneanilines based on quantum chemical parameters and radial basis function neural network.

Based on quantum chemical parameters and a simple numerical coding, the liquid chromatography retention of bifunctionally substituted N-benzylideneaniles (NBA) has been predicted using a radial basis function neural network (RBFNN) model. The quantum chemical parameters involved in the model are dipole moment (m), energies of the highest occupied and lowest unoccupied molecular orbitals (E(homo,) E(lumo)), net charge of the most negative atom (Q(min)), sum of absolute values of the charges of all atoms in two given functional groups (Delta), total energy of the molecule (E(T)), weight of the molecule (W), and numerical coding (N). N was used to indicate the different positions of two substituents. The predictive values are consistent with the experimental results. The mean relative error of the testing set is 1.6%, and the maximum relative error is less than 5.0%. In this work the success of the whole modeling process only depends on the optimization of the spread parameter in network.

Journal Article↗

PubMed1995

A radial basis function model of muscle stimulated with irregular inter-pulse intervals.

Paralysed muscle, or skeletal muscle which is to be used for cardiac assistance, may be given an artificial function if it is electrically stimulated to contract and the response can be adequately controlled. To design a controller, a model of the muscle or system is usually required. The most commonly used models are analogues, originating from A.V. Hill's model. However muscles exhibit many nonlinear and time-varying phenomena which, if they are to be modelled, make the analogue complex and cumbrous to work with. The system may further be complicated by pathological changes and secondary effects of stimulation. We propose that such a system can be modelled by nonlinear networks ('neural networks'). The radial basis function network (RBF) has two advantages over the better-known multi-layer perceptron (MLP). We describe the use of an RBF network to model rabbit muscle that is supramaximally stimulated at irregular inter-pulse intervals.

Animals↗

PubMed2001

Prediction of enthalpy of alkanes by the use of radial basis function neural networks.

A new method for the prediction of enthalpy of alkanes between C6 and C10 from molecular structures has been proposed. Thirty five calculated descriptors were selected for the description of molecular structures. The first four scores of Principle Component Analysis on the calculated descriptors were used as inputs to predict the enthalpy of alkanes. Models relating relationships between molecular structure descriptors and enthalpy of alkanes were constructed by means of radial basis function neural networks. To get the best prediction results, some strategies were also employed to optimise the learning parameters of the radial basis function neural networks. For the test set, a predictive correlation coefficient of R = 0.9913 and root mean squared error of 0.5876 were obtained.

Journal Article↗

PubMed1997

A sequential learning scheme for function approximation using minimal radial basis function neural networks.

This article presents a sequential learning algorithm for function approximation and time-series prediction using a minimal radial basis function neural network (RBFNN). The algorithm 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 RBFNN. The performance of the algorithm is compared with RAN and the enhanced RAN algorithm of Kadirkamanathan and Niranjan (1993) for the following benchmark problems: (1) hearta from the benchmark problems database PROBEN1, (2) Hermite polynomial, and (3) Mackey-Glass chaotic time series. For these problems, the proposed algorithm is shown to realize RBFNNs with far fewer hidden neurons with better or same accuracy.

Algorithms↗

PubMed2002

Hierarchical genetic algorithm for near optimal feedforward neural network design.

In this paper, we propose a genetic algorithm based design procedure for a multi layer feed forward neural network. A hierarchical genetic algorithm is used to evolve both the neural networks topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi layer Perceptron networks and radial basis function networks. Based upon the chosen cost function, a linear weight combination decision making approach has been applied to derive an approximated Pareto optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two objective optimization problem.

Algorithms↗

PubMed2005

Prediction of inter-residue contacts map based on genetic algorithm optimized radial basis function neural network and binary input encoding scheme.

Inter-residue contacts map prediction is one of the most important intermediate steps to the protein folding problem. In this paper, we focus on the problem of protein inter-residue contacts map prediction based on neural network technique. Firstly, we use a genetic algorithm (GA) to optimize the radial basis function widths and hidden centers of a radial basis function neural network (RBFNN), then a novel binary encoding scheme is employed to train the network for the purpose of learning and predicting the inter-residue contacts patterns of protein sequences got from the protein data bank (PDB). The experimental evidence indicates the utility of our proposed encoding strategy and GA optimized RBFNN. Moreover, the simulation results demonstrate that the network got a better performance for these proteins, whose residue length falls into the area of (100, 300), and the predicted accuracy with a contact threshold of 7 Angstroms scores higher than the other 3 values with 5, 6, and 8 Angstroms.

Algorithms↗

PubMed2001

Drug design by machine learning: support vector machines for pharmaceutical data analysis.

We show that the support vector machine (SVM) classification algorithm, a recent development from the machine learning community, proves its potential for structure-activity relationship analysis. In a benchmark test, the SVM is compared to several machine learning techniques currently used in the field. The classification task involves predicting the inhibition of dihydrofolate reductase by pyrimidines, using data obtained from the UCI machine learning repository. Three artificial neural networks, a radial basis function network, and a C5.0 decision tree are all outperformed by the SVM. The SVM is significantly better than all of these, bar a manually capacity-controlled neural network, which takes considerably longer to train.

Algorithms↗