Radial Basis Function Parameters Research Articles

Support Vector Machine algorithm optimal parameterization for change detection mapping in Funil Hydroelectric Reservoir (Rio de Janeiro State, Brazil)

Change detection in Land Use and Land Cover (LULC) using Support Vector Machines (SVM) to mapping a geographic area is a way that has been studded and improved because of its advantages as low costs in terms of computing, field research and staff team. To use SVM, it is needed firstly to define the most efficient function to be used (linear, polynomial, and radial base function—RBF) and secondly to establish the most appropriate input parameters of them, based on the study area, which was the main challenge of using SVM algorithm. The main goal of this work was to test the performance of polynomial function and RBF, and to identify which input parameters combination are the best to use SVM algorithm for Funil Hydroelectric Reservoir (FHR) sub-watershed LULC mapping, using TM/Landsat-5 time-series images. After several tests and based on the obtained results, the RBF was identified as the best SVM’s function, which was used to classify the time-series images. The referred SVM function has the following parameters to be defined: the error tolerance (ξ or C), the pyramid depths (P), the radial basis function parameter (γ), and the threshold. The most effective combination of input parameters to RBF was C = 100; P = 2, γ = 0.1, threshold = 0.05. LULC change detection analyses demonstrates that the obtained SVM parameterization made the algorithm able to differentiate large and continuous classes, lengthy and thin areas, as borders, and not continuous small areas located inside wide classes, through the usage of effective, but small, training sample. The parameterization proposed for this work to FHR sub-watershed area resulted in great statistics classification with the overall’s accuracy among 86 and 98 % over the time-series, the producer’s accuracy of 90 %, the user’s accuracy higher than 86 %, and the Kappa statistics ranged from 86 to 91 %.

Point Set Denoising Using Bootstrap-Based Radial Basis Function

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study.

A numerically efficient technique of regional gravity field modeling using Radial Basis Functions

Radial Basis Functions (RBFs) have been extensively used in regional gravity and (quasi)geoid modeling. Reliable models require the choice of an optimal number of RBFs and of their parameters. The RBF parameters are typically optimized using a regularization algorithm. Therefore, the determination of the number of RBFs is the most challenging task in the modeling procedure. For this purpose, we design a data processing scheme to optimize the number of RBFs and their parameters simultaneously. Using this scheme, the gravimetric quasi-geoid model can be validated without requiring additional information on the quasi-geoidal geometry obtained from GPS/leveling data. Furthermore, the Levenberg–Marquardt algorithm, used for regularization, is modified to enhance its numerical performance. We demonstrate that these modifications guarantee the convergence of the solution to the global minimum while substantially decreasing the number of iterations. The proposed methodology is evaluated using synthetic gravity data and compared with existing methods for validating the RBF parameterization of the gravity field.

Novel hybrid soft computing pattern recognition system SVM–GAPSO for classification of eight different hand motions

In this manuscript, we proposed an intelligent hybrid pattern recognition system to classify eight hand motions. Two evolutionary algorithms: genetic algorithm (GA) and particle swarm optimization (PSO) were combined with support vector machine (SVM) to construct a novel model (GAPSO–SVM). The proposed hybrid system able to obtain a high performance in handling learning task with SVM by selecting the optimal parameters of radial basis function (RBF–SVM) and choosing the optimal decomposition level of the mother wavelet function. In this study, energy of wavelet coefficients (EWC) were extracted from surface electromyographic (sEMG) signals, which collected from forearm's muscles. Moreover, due to the reason that the effectiveness of myoelectric pattern recognition system also depends on the degree of dimensionality reduction of the selected feature vector (FV), we investigated the performance of different feature projection algorithms: neighborhood preserving embedding (NPE), principle component analysis (PCA), independent components analysis (ICA) and orthogonal linear discriminant analysis (OLDA). The result shows that the proposed hybrid model predicts with greater accuracy and reliability in comparison to other three classifiers: support vector machines (SVM), fuzzy least squares support vector machines (LS–SVM) and K-nearest neighbor (K-NN). The highest achieved average accuracy rate was 98.7% by employing SVM-GAPSO classifier based on PCA.

Construct ‘FE-Meshfree’ Quad4 using mean value coordinates

The present work uses mean value coordinates to construct the shape functions of a hybrid ‘FE-Meshfree’ quadrilateral element, which is named as Quad4-MVC. This Quad4-MVC can be regarded as the development of the ‘FE-Meshfree’ quadrilateral element with radial-polynomial point interpolation (Quad4-RPIM). Similar to Quad4-RPIM, Quad4-MVC has Kronecker delta property on the boundaries of computational domain, so essential boundary conditions can be enforced as conveniently as in the finite element method (FEM). The novelty of the present work is to construct nodal approximations using mean value coordinates, instead of radial basis functions which are used in Quad4-RPIM. Compared to the radial basis functions, mean value coordinates does not utilize any uncertain parameters, which enhances stability of numerical results. Numerical tests in this paper show that the performance of Quad4-RPIM becomes even worse than four-node iso-parametric element (Quad4) when the parameters of radial basis functions are not chosen properly. However, the performance of Quad4-MVC is stably better than Quad4.

RBFNs Nonlinear Control System Design through BFPSO Algorithm

All parameters are automatically extracted by the bacterial foraging particle swarm optimization (BFPSO) algorithm to approach the desired control system. Three parameterize basis function neural networks (RBFNs) model to solve the car-pole system problem. Several free parameters of radial basis functions can be automatically tuned by the direct of the specified fitness function. In additional, the proper number of radial basis functions (RBFs) of the constructed RBFNs can be chosen by the defined fitness function which takes this factor into account. The desired multiple objectives of the RBFNs control system are proposed to simultaneously approach the smaller errors with a fewer RBFs number. Simulations show that the developed RBFNs control systems efficiently achieve the desired the setting lot as soon as possible.

Optimal variable shape parameters using genetic algorithm for radial basis function approximation

Many radial basis function (RBF) methods contain free shape parameter or parameters that play an important role for the accuracy of the method. In most papers the authors end up choosing free shape parameter by trial and error or some other ad-hoc means. However, using variable shape parameters provides a clear potential for improved accuracy and stability of the RBF method. Already some progress has been reported to select usable variable shape parameters. In this paper, we propose applying the genetic algorithm to determine good variable shape parameters of radial basis functions for the solution of ordinary differential equations. Numerical results show that the proposed algorithm based on the genetic optimization is effective and provides reasonable shape parameters along with acceptable accuracy in linear and nonlinear case compared with other strategies to determine variable shape parameters.

Shape Parameter Optimization of Gaussian Radial Basis Function Using Genetic Algorithm for Natural Frequencies of Laminated Composite Plates

Natural frequencies of simply supported laminated composite plates are calculated by the meshless global collocation method based on Gaussian radial basis function. The accuracy of meshless global radial basis function collocation method depends on the choice of shape parameter of radial basis function. In present paper, the shape parameter of Gaussian radial basis function is optimized using the genetic algorithm. Gaussian radial basis function with optimal shape parameter is utilized to analyze the natural frequencies of simply supported laminated composite plates. The present results are compared with the results of available literatures which verify the accuracy of present method.

Shape Parameter Optimization of Inverse Multiquadrics Radial Basis Function for Vibration of Laminated Composite Plates

Free vibration of simply laminated composite plates is studied by the global collocation method based on inverse multiquadrics radial basis function. The choice of shape parameter of radial basis function has the important effect on the accuracy of meshless radial basis function collocation method. Genetic algorithm is used to optimize the shape parameter of inverse multiquadrics radial basis function. The natural frequencies of simply supported laminated composite plates are calculated using the inverse multiquadrics radial basis function with optimal shape parameter and compared with the analytical solutions.

The classification of underwater acoustic target signals based on wave structure and support vector machine

The sound of propeller is a remarkable feature of ship-radiated noise, the loudness and timbre of which are usually applied to identify types of ships. Since the information of loudness and timbre is indicated in the wave structure of time series, the feature of wave structure can be extracted to classify types of various underwater acoustic targets. In this paper, the method of feature vector extraction of underwater acoustic signals based on wave structure is studied. The nine-dimension features are constructed via signal statistical characteristics of zero-crossing wavelength, peek-to-peek amplitude, zero-crossing wavelength difference, and wave train areas. And then, the support vector machine (SVM) is applied as a classifier for two kinds of underwater acoustic target signals. The kernel function is set radial basis function (RBF). By properly setting the penalty factor and parameter of RBF, the recognition rate reaches over 89.5%, respectively. The sea-test data shows the validity of target recognition ability of the method above.

Support vector machine to map oil palm in a heterogeneous environment

Support vector machines (SVMs) have been frequently shown to result in more accurate classification than other image classification methods. However, few studies have successfully quantified their performance for mapping oil palm plantations. Various sustainability criteria developed by the Round Table on Sustainable Palm Oil (RSPO) have a spatial component but they provide little guidance on mapping oil-palm-related cover changes. SVM and maximum likelihood classifier (MLC) classification approaches in classifying oil palm plantations with Landsat ETM+ were compared. The best combination of three bands from the satellite image was selected based on Bhattacharyya distance. SVM and MLC performance was evaluated using overall accuracy assessment and kappa statistics. Bands 4, 5, and 3 provided the best spectral separability indices based on Bhattacharyya distance. SVM classification resulted in an overall accuracy of 78.3% (kappa statistic 0.73) compared with MLC, with an overall accuracy of 71.9% (kappa statistic 0.65). The performance of the SVM method is mainly affected by the accurate setting of parameters involved in the algorithm. The radial basis function parameter setting in SVM was an important variable in the classification process, and SVM improved the classification of oil palm mapping. Although the classification accuracy is still insufficient for large-scale implementation of the technique, further refinements may provide a way forward towards producing baseline information useful for RSPO certification.

Instability identification on large scale underground mined-out area in the metal mine based on the improved FRBFNN

To identify the instability on large scale underground mined-out area in the metal mine effectively, the parameters of radial basis function were determined through clustering method and the improved fuzzy radial basis function neural network (FRBFNN) model of instability identification model about large scale underground mined-out area in the metal mine was built. The improved FRBFNN model was trained and tested. The results show that the improved FRBFNN model has high training accuracy and generalization ability. Parameters such as pillar area ratio, filling level and the value of rock quality designation have strong influence on instability of large scale underground mined-out area. Correctness of analysis about the improved FRBFNN model was proved by the practical application results about instability discrimination of surrounding rock in large-scale underground mined-out area of a metal mine in south China.

Radial basis function method applied to doubly-curved laminated composite shells and panels with a General Higher-order Equivalent Single Layer formulation

The aim of this work is the application of Radial Basis Function (RBF) method to a General Higher-order Equivalent Single Layer (GHESL) formulation for the free vibrations of doubly-curved laminated composite shells and panels. The theoretical development of the present paper is based on the well-known Carrera Unified Formulation. In particular, the fundamental nuclei of a multi-layered doubly-curved shell structure are deducted and explicitly defined. The Differential Geometry (DG) tool has been used to geometrically define each of the structures under consideration: doubly-curved, singly-curved and degenerate shells. The 2D free vibration shell problems are numerically solved using RBFs, where the shape parameters have been optimized using two different algorithms. In fact, the shape parameters of RBFs depend not only on the choice of the radial basis functions, but also on how the points are located on the given computational domain. Modifying the positions of such points, the shape parameters change too. It has been discovered that, once the shape parameters have been optimized for a given grid distribution, they can be rounded off and used for every kind of structure. This is a very important aspect because when, using a fixed parameter, the RBF method becomes a “parameter free” numerical technique. In order to demonstrate the accuracy, stability and reliability of the present methodology, many comparisons are presented with reference to literature results, that are obtained by using Generalized Differential Quadrature method. The above numerical applications of this study are also compared with finite element method solutions.

Nonlinear Fitting Characteristics Analysis on Prediction Model of Adaptive Variable Weight Fuzzy RBF Neural Network

For the number and width of the implicit layer RBF centers have a direct impact on the approximation capability of RBF neural network, clustering method is adopted to determine the radial basis function parameters, adaptive variable weight method is used to improve the conventional fuzzy RBF neural network learning algorithm, adaptive variable weight fuzzy RBF neural network prediction model is built, and simulation experiments are performed on its non-linear function approximation performance. Results show that the adaptive variable weight fuzzy RBF neural network prediction model has high accuracy in both single-input single-output nonlinear prediction and multiple-input multiple-output nonlinear prediction. Instability analysis results of surrounding rock in a massive metal mine gob area in southern China verify the effectiveness and practicality of the nonlinear fitting of the model.

Automated Cardiac Beat Classification Using RBF Neural Networks

This paper proposes a four stage, denoising, feature extraction, optimization and classification method for detection of premature ventricular contractions. In the first stage, we investigate the application of wavelet denoising in noise reduction of multi-channel high resolution ECG signals. In this stage, the Stationary Wavelet Transform is used. Feature extraction module extracts ten ECG morphological features and one timing interval feature. Then a number of radial basis function (RBF) neural networks with different value of spread parameter are designed and compared their ability for classification of three different classes of ECG signals. Genetic Algorithm is used to find best value of RBF parameters. A classification accuracy of 100% for training dataset and 95.66% for testing dataset and an overall accuracy of detection of 95.83% were achieved over seven files from the MIT/BIH arrhythmia database.

Self-Tuning RBFNs Mobile Robot Systems through Bacterial Foraging Particle Swarm Optimization Learning Algorithm

A radial basis function neural networks (RBFNs) mobile robot control system is automatically developed with the image processing and learned by the bacterial foraging particle swarm optimization (BFPSO) algorithm in this paper. The image-based architecture of robot model is self-generated to travel the routing path in the dynamical and complicated environments. The visible omni-directional image sensors capture the surrounding environment to represent the behavior model of the mobile robot system. Three parameterize RBFNs model with the centers and spreads of each radial basis function, and the connection weights to solve the mobile robot path traveling and routing problems. Several free parameters of radial basis functions can be automatically tuned by the direct of the specified fitness function. In additional, the proper number of radial basis functions of the constructed RBFNs can be chosen by the defined fitness function which takes this factor into account. The desired multiple objectives of the RBFNs control system are proposed to simultaneously approach the shorter path and avoid the unexpected obstacles. Evaluations of PSO and BFPSO show that the developed RBFNs robot systems skip the obstacles and efficiently achieve the desired targets as soon as possible.

A clinical decision support system for femoral peripheral arterial disease treatment.

One of the major challenges of providing reliable healthcare services is to diagnose and treat diseases in an accurate and timely manner. Recently, many researchers have successfully used artificial neural networks as a diagnostic assessment tool. In this study, the validation of such an assessment tool has been developed for treatment of the femoral peripheral arterial disease using a radial basis function neural network (RBFNN). A data set for training the RBFNN has been prepared by analyzing records of patients who had been treated by the thoracic and cardiovascular surgery clinic of a university hospital. The data set includes 186 patient records having 16 characteristic features associated with a binary treatment decision, namely, being a medical or a surgical one. K-means clustering algorithm has been used to determine the parameters of radial basis functions and the number of hidden nodes of the RBFNN is determined experimentally. For performance evaluation, the proposed RBFNN was compared to three different multilayer perceptron models having Pareto optimal hidden layer combinations using various performance indicators. Results of comparison indicate that the RBFNN can be used as an effective assessment tool for femoral peripheral arterial disease treatment.

Response Surface Method Based on Radial Basis Functions for Modeling Large‐Scale Structures in Model Updating

Abstract: The response surface (RS) method based on radial basis functions (RBFs) is proposed to model the input–output system of large‐scale structures for model updating in this article. As a methodology study, the complicated implicit relationships between the design parameters and response characteristics of cable‐stayed bridges are employed in the construction of an RS. The key issues for application of the proposed method are discussed, such as selecting the optimal shape parameters of RBFs, generating samples by using design of experiments, and evaluating the RS model. The RS methods based on RBFs of Gaussian, inverse quadratic, multiquadric, and inverse multiquadric are investigated. Meanwhile, the commonly used RS method based on polynomial function is also performed for comparison. The approximation accuracy of the RS methods is evaluated by multiple correlation coefficients and root mean squared errors. The antinoise ability of the proposed RS methods is also discussed. Results demonstrate that RS methods based on RBFs have high approximation accuracy and exhibit better performance than the RS method based on polynomial function. The proposed method is illustrated by model updating on a cable‐stayed bridge model. Simulation study shows that the updated results have high accuracy, and the model updating based on experimental data can achieve reasonable physical explanations. It is demonstrated that the proposed approach is valid for model updating of large and complicated structures such as long‐span cable‐stayed bridges.

Detection of Rice Exterior Quality based on Machine Vision

To investigate the detection of rice exterior quality, a machine vision system was developed. The main characteristics of rice appearance including area, perimeter, roughness and minimum enclosing rectangle were calculated by image analysis. Least Squares Support Vector Machines, Naive Bayes Classifier and Back Propagation Artificial Neural Network were applied to achieve classification of head rice and broken rice, and the classification results of three algorithms were analyzed in detail. Genetic algorithm and Particle Swarm Optimization were used to obtain the optimal values of regularization parameter and kernel radial basis function parameter, and adopt a supervised learning approach to train the Least Squares Support Vector Machines model. Meanwhile the robustness of these classification methods was tested, and the results shows that support vector machine have better classification results in this experiment. This study demonstrated the feasibility of detection rice quality using machine vision. Keywords; Rice, Machine Vision, LS-SVM, Classification, Image Processing

A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems

The boundary face method is coupled with the dual reciprocity method (DRM) to solve non-homogeneous elasticity problems. We will analyze thin structures based on 3D solid elastic theory rather than the shell theory as in the finite element method (FEM). To circumvent the ill-conditioning problem that occurs in the radial basis function (RBF) approximation in thin structures, a special variation scheme for determining the RBF parameters is proposed. In addition, a new exponential RBF is used which has significantly improved the stability of the RBF, and its particular solution to the elasticity problem is derived for the first time. Comparisons of our method with the traditional DRM, the boundary element method (BEM) and the FEM have been made. Numerical examples have demonstrated that our method outperforms the BEM and FEM with respect to stability, accuracy and efficiency, especially when the structure in question has features of small size, such as thin shells.