Generalized Radial Basis Function Research Articles

Characterizing Trabecular Bone structure for Assessing Vertebral Fracture Risk on Volumetric Quantitative Computed Tomography.

While the proximal femur is preferred for measuring bone mineral density (BMD) in fracture risk estimation, the introduction of volumetric quantitative computed tomography has revealed stronger associations between BMD and spinal fracture status. In this study, we propose to capture properties of trabecular bone structure in spinal vertebrae with advanced second-order statistical features for purposes of fracture risk assessment. For this purpose, axial multi-detector CT (MDCT) images were acquired from 28 spinal vertebrae specimens using a whole-body 256-row CT scanner with a dedicated calibration phantom. A semi-automated method was used to annotate the trabecular compartment in the central vertebral slice with a circular region of interest (ROI) to exclude cortical bone; pixels within were converted to values indicative of BMD. Six second-order statistical features derived from gray-level co-occurrence matrices (GLCM) and the mean BMD within the ROI were then extracted and used in conjunction with a generalized radial basis functions (GRBF) neural network to predict the failure load of the specimens; true failure load was measured through biomechanical testing. Prediction performance was evaluated with a root-mean-square error (RMSE) metric. The best prediction performance was observed with GLCM feature 'correlation' (RMSE = 1.02 ± 0.18), which significantly outperformed all other GLCM features (p < 0.01). GLCM feature correlation also significantly outperformed MDCT-measured mean BMD (RMSE = 1.11 ± 0.17) (p < 10-4). These results suggest that biomechanical strength prediction in spinal vertebrae can be significantly improved through characterization of trabecular bone structure with GLCM-derived texture features.

Speaker identification using multimodal neural networks and wavelet analysis

The rapid momentum of the technology progress in the recent years has led to a tremendous rise in the use of biometric authentication systems. The objective of this research is to investigate the problem of identifying a speaker from its voice regardless of the content. In this study, the authors designed and implemented a novel text-independent multimodal speaker identification system based on wavelet analysis and neural networks. Wavelet analysis comprises discrete wavelet transform, wavelet packet transform, wavelet sub-band coding and Mel-frequency cepstral coefficients (MFCCs). The learning module comprises general regressive, probabilistic and radial basis function neural networks, forming decisions through a majority voting scheme. The system was found to be competitive and it improved the identification rate by 15% as compared with the classical MFCC. In addition, it reduced the identification time by 40% as compared with the back-propagation neural network, Gaussian mixture model and principal component analysis. Performance tests conducted using the GRID database corpora have shown that this approach has faster identification time and greater accuracy compared with traditional approaches, and it is applicable to real-time, text-independent speaker identification systems.

A Hybrid Intelligent System Approach to Forecasting of PV Generation Output

In this paper, a hybrid intelligent method is proposed to deal with the prediction of PV generation output. It is important to predict PV generation output with high accuracy and smooth operational planning. The proposed method integrates Generalized Radial Basis Function Network (GRBFN) of Artificial Neural Network (ANN) with Deterministic Annealing (DA) clustering of globally optimal clustering to improve the performance of the conventional Radial Basis Function Network (RBFN). The use of DA is effective for determining better initial values of the GRBFN parameters. In practice, GRBFN outperforms RBFN in a way that the parameters of the radial basis function are determined by the learning process. The effectiveness of the proposed method is demonstrated in real data.

Analysis of supersonic separators geometry using generalized radial basis function (GRBF) artificial neural networks

Supersonic separators (3S) are comprised from unique combination of known physical processes, combining aero-dynamics, thermo-dynamics and fluid-dynamics to produce an innovative gas conditioning process. Condensation and separation at supersonic velocity is the key to achieve a significant reduction in both capital and operating costs. Natural gas dehydration, ethane extraction, LPG production and natural gas sweetening are some potential applications of 3S units among many others. Feed-forward artificial neural networks (ANNs) are also powerful tools for empirical modeling of various engineering processes. Generalized radial basis function (GRBF) networks which are kernel based ANNs, have the best approximation property since they represent the optimal solution of multivariate linear regularization theory. A large set of synthetic data are generated in this work via the fundamental modeling of 3S units and are used to train an optimal GRBF network. The trained network is then used to properly design two pilot and industrial scale 3S units for natural gas dehumidification processes. Furthermore, the trained network is successfully and much more rapidly used for trend analysis purposes to investigate the effect of various input parameters. The conducted research clearly demonstrates the acceptable performance of such neural networks for both design and trend analysis purposes.

A novel self-constructing Radial Basis Function Neural-Fuzzy System

This paper proposes a novel self-constructing least-Wilcoxon generalized Radial Basis Function Neural-Fuzzy System (LW-GRBFNFS) and its applications to non-linear function approximation and chaos time sequence prediction. In general, the hidden layer parameters of the antecedent part of most traditional RBFNFS are decided in advance and the output weights of the consequent part are evaluated by least square estimation. The hidden layer structure of the RBFNFS is lack of flexibility because the structure is fixed and cannot be adjusted effectively according to the dynamic behavior of the system. Furthermore, the resultant performance of using least square estimation for output weights is often weakened by the noise and outliers.This paper creates a self-constructing scenario for generating antecedent part of RBFNFS with particle swarm optimizer (PSO). For training the consequent part of RBFNFS, instead of traditional least square (LS) estimation, least-Wilcoxon (LW) norm is employed in the proposed approach to do the estimation. As is well known in statistics, the resulting linear function by using the rank-based LW norm approximation to linear function problems is usually robust against (or insensitive to) noises and outliers and therefore increases the accuracy of the output weights of RBFNFS. Several nonlinear functions approximation and chaotic time series prediction problems are used to verify the efficiency of self-constructing LW-GRBFNIS proposed in this paper. The experimental results show that the proposed method not only creates optimal hidden nodes but also effectively mitigates the noise and outliers problems.

A GRBFN-EPSO-based Method for Predicting PV Generation Output

In this paper, a new method is presented to predicting PV generation output. The method makes use of a hybrid intelligent system of EPSO (Evolutionary Particle Swarm Optimization) of meta heuristics and GRBFN (Generalized Radial Basis Function Network) of artificial neural network (ANN). GRBFN is an extension of RBFN in a sense that the center and the width of the radial basis functions are determined by the learning process although the conventional RBFN does not update them through the learning process. EPSO is used to evaluate better the weights between the hidden and the output layers because it is useful for solving nonlinear optimization problems from a standpoint of global optimization. In particular, EPSO has advantage to adjust the algorithm parameters with the evolutionary strategy to make the search process more diverse by the replication. In addition, DA (Deterministic Annealing) clustering that corresponds to a global clustering technique is employed to evaluate the initial solutions of the center and the width so that the performance of GRBFN is improved. Furthermore, the weight decay method is utilized at the learning processes to avoid the overfitting to learning data since the conventional methods are inclined to provide erroneous results due to overfitting to complicated time series data of PV generation output. The proposed method is successfully applied to real data of a PV system.

Radial basis function regularization for linear inverse problems with random noise

In this paper, we study the statistical properties of the method of regularization with radial basis functions in the context of linear inverse problems. Radial basis function regularization is widely used in machine learning because of its demonstrated effectiveness in numerous applications and computational advantages. From a statistical viewpoint, one of the main advantages of radial basis function regularization in general and Gaussian radial basis function regularization in particular is their ability to adapt to varying degrees of smoothness in a direct problem. We show here that similar approaches for inverse problems not only share such adaptivity to the smoothness of the signal but also can accommodate different degrees of ill-posedness. These results render further theoretical support to the superior performance observed empirically for radial basis function regularization.

Permanent disability classification by combining evolutionary Generalized Radial Basis Function and logistic regression methods

Recently, a novelty multinomial logistic regression method where the initial covariate space is increased by adding the nonlinear transformations of the input variables given by Gaussian Radial Basis Functions (RBFs) obtained by an evolutionary algorithm was proposed. However, there still exist some problems with the standard Gaussian RBF, for example, the approximation of constant valued functions or the approximation of high dimensionality associated to some real problems. In order to face these problems, we propose the use of the generalized Gaussian RBF (GRBF) instead of the standard Gaussian RBF. Our approach has been validated with a real problem of disability classification, to evaluate its effectiveness. Experimental results show that this approach is able to achieve good generalization performance.

Evolutionary Generalized Radial Basis Function neural networks for improving prediction accuracy in gene classification using feature selection

Radial Basis Function Neural Networks (RBFNNs) have been successfully employed in several function approximation and pattern recognition problems. The use of different RBFs in RBFNN has been reported in the literature and here the study centres on the use of the Generalized Radial Basis Function Neural Networks (GRBFNNs). An interesting property of the GRBF is that it can continuously and smoothly reproduce different RBFs by changing a real parameter τ. In addition, the mixed use of different RBF shapes in only one RBFNN is allowed. Generalized Radial Basis Function (GRBF) is based on Generalized Gaussian Distribution (GGD), which adds a shape parameter, τ, to standard Gaussian Distribution. Moreover, this paper describes a hybrid approach, Hybrid Algorithm (HA), which combines evolutionary and gradient-based learning methods to estimate the architecture, weights and node topology of GRBFNN classifiers. The feasibility and benefits of the approach are demonstrated by means of six gene microarray classification problems taken from bioinformatic and biomedical domains. Three filters were applied: Fast Correlation-Based Filter (FCBF), Best Incremental Ranked Subset (BIRS), and Best Agglomerative Ranked Subset (BARS); this was done in order to identify salient expression genes from among the thousands of genes in microarray data that can directly contribute to determining the class membership of each pattern. After different gene subsets were obtained, the proposed methodology was performed using the selected gene subsets as new input variables. The results confirm that the GRBFNN classifier leads to a promising improvement in accuracy.

New Method of Diagnosis and New Knowledge Acquirement for Fault Diagnosis Expert System of High Voltage Circuit Breaker

In this paper, an improved algorithm of general radial basis (RBF) function neural network is introduced, based on improved algorithm, the neural network realized quickly fault diagnosis and self-update of neural network structure, and the neural network is applied to the on-line fault diagnosis expert system. The expert system deals with the fault data that send from on-line monitoring equipment by using neural network, and it can discover the fault type and give reasonable solution by forward reasoning. Meanwhile, the expert system has the ability of achieving new knowledge based on the application of self-update ability of RBF neural network.

General Regression Neural Network and Radial Basis Neural Network for the Estimation of Crop Variables of Lady Finger

Estimation of crop variables is necessary for crop type monitoring as well as crop yield forecast. At the present era artificial neural network methodology are widely used to the remote sensing domain for numerous applications like crop yield forecasting and crop type classification. In the present work, two neural network models namely general regression neural network (GRNN) and radial basis function neural network (RBFNN) are used to estimate crop variables: leaf area index (LAI), biomass (BM), plant height (PH) and soil moisture (SM) by using ground based X-band scatterometer data. The both networks are trained and tested with X-band scatterometer data. The performance of the GRNN and RBFNN networks are found that the radial basis approach is more suitable for crop variable estimation in comparison to the GRNN approach. This work presents the applicability of neural network as an estimator and method employed could be useful to estimate the crop variables of other crops.

Fuzzy-C-Mean Based Radial Basis Function Network Application in Machinery Noise Prediction

Advanced mechanized in opencast mines in now-a-days expected to intensify more noise problems in working environment. Prolonged exposure of miners to the high levels of noise can cause noise induced hearing loss besides several non-auditory health effects. To maintain the good working environment in mines, appropriate noise survey of machineries should be conducted. Hence in order to improve the environmental condition in working place, it is needed to develop appropriate noise prediction model for finding out the accurate status of noise levels from various surface mining machineries. The measured sound pressure level (SPL) of equipments is not accurate due to instrumental error, attenuation, geometrical aberration, atmospheric attenuation etc. Some of the popular noise prediction models e.g. ISO: 9613-2, ENM, CONCAWE have been applied in mining and allied industries. In this paper, an advanced radial basis neural network (RBFN) has been proposed. Two types of RBFN architectures: Generalized Radial Basis Function Network (GRBFN) and Fuzzy-C-Mean based Radial Basis Function Network (FCMRBFN) were used to predict the machinery noise in a large opencast bauxite mine. The proposed models were designed with ISO: 9613-2 noise prediction guidelines considering 1/1 octave band. From the present investigation, it can be concluded that, the output of FCMRBFN system based noise prediction models closely matches with the ISO: 9613-2 model output.

Neuro-logistic Models Based on Evolutionary Generalized Radial Basis Function for the Microarray Gene Expression Classification Problem

Gene expression detection is a key bioinformatic problem which has been tackled as a classification problem of microarray gene expression, obtained by the light reflection analysis of genomic material. A typical microarray dataset may contain thousands of genes but only a small number of patterns (often less than two hundred). When the dataset presents these kinds of characteristics, state-of-the-art classification models show a high lack of performance. A two-stage algorithm has been proposed to successfully address the problem of microarray classification. In the first stage, two filter algorithms identify salient expression genes from thousands of genes. In the second stage, the proposed methodology is performed using selected gene subsets as new input variables. The methodology proposed is composed of a combination of Logistic Regression (LR) and Evolutionary Generalized Radial Basis Function (EGRBF) neural networks which have shown to be highly accurate in previous research in the modeling of high-dimensional patterns. Finally, the results obtained are contrasted with nonparametric statistical tests and confirm good synergy between EGRBF and LR models.

MELM-GRBF: A modified version of the extreme learning machine for generalized radial basis function neural networks

In this paper, we propose a methodology for training a new model of artificial neural network called the generalized radial basis function (GRBF) neural network. This model is based on generalized Gaussian distribution, which parametrizes the Gaussian distribution by adding a new parameter τ . The generalized radial basis function allows different radial basis functions to be represented by updating the new parameter τ . For example, when GRBF takes a value of τ = 2 , it represents the standard Gaussian radial basis function. The model parameters are optimized through a modified version of the extreme learning machine (ELM) algorithm. In the methodology proposed (MELM-GRBF), the centers of each GRBF were taken randomly from the patterns of the training set and the radius and τ values were determined analytically, taking into account that the model must fulfil two constraints: locality and coverage. An thorough experimental study is presented to test its overall performance. Fifteen datasets were considered, including binary and multi-class problems, all of them taken from the UCI repository. The MELM-GRBF was compared to ELM with sigmoidal, hard-limit, triangular basis and radial basis functions in the hidden layer and to the ELM-RBF methodology proposed by Huang et al. (2004) [1]. The MELM-GRBF obtained better results in accuracy than the corresponding sigmoidal, hard-limit, triangular basis and radial basis functions for almost all datasets, producing the highest mean accuracy rank when compared with these other basis functions for all datasets.

A Moderate Algorithm for Generalized Radial basis Function Neural Networks

Radial Basis Function (RBF) neural network can be regarded as a feed forward network composed of multiple layers of neurons with entirely different roles. The input layer made of sensory units that connect the network to its environment. A radial basis function neural network depends mainly upon an adequate choice of the number and positions of its basis function centers. In case of generalized RBF neural network, the output layer is linear and supplying each layer response as the linear combination of the hidden responses. In this paper we have proposed a moderate algorithm for most generalized form of RBF neural network and the results may be reduced for various forms of RBF and other artificial neural networks as particular cases.

Multiscale Combined Radial Basis Function Collocation Method for Eddy Currents Analysis in High-Speed Moving Conductors

A novel multiscale combined radial basis function (RBF) collocation method, as a truly meshless method, is presented to overcome the shortage of general RBF collocation method and is applied to analyze eddy currents in high-speed moving conductors in this paper. A typical example is set here to illustrate the accuracy and affectivity of the proposed method, including a comparison with general RBF collocation method and finite element method (FEM).

Adaptive neural-networks-based fault detection and diagnosis using unmeasured states

Fault detection and diagnosis play important roles in modern engineering systems. A number of fault diagnosis (FD) approaches for nonlinear systems have been proposed. But, most of the achievements are based on the assumptions that the systems models are known, and states of systems are measurable. A novel FD architecture for a class of unknown nonlinear systems with unmeasured states has been investigated. A general radial basis function (RBF) neural network is used to approximate the model of unknown system, an adaptive RBF neural network with on-line updated centre, and the width vector of ‘Gaussian’ function is used to approximate the model of fault. A nonlinear state observer is designed to estimate system states that are inputs to the neural networks. The stability analysis for the system is given, and the adaptive parameter-updating laws are derived using Lyapunov theory. Simulation examples are used to illustrate the effectiveness of the proposed method.

Adaptive Processing of Range Scanned Head: Synthesis of Personalized Animated Human Face Representation with Multiple-Level Radial Basis Function

We propose an animation system for personalized human head. Landmarks compliant to MPEG-4 facial definition parameters (FDP) are initially labeled on both template model and any target human head model as priori knowledge. The deformation from the template model to the target head is through a multilevel training process. Both general radial basis function (RBF) and compactly supported radial basis function (CSRBF) are applied to ensure the fidelity of the global shape and face features. Animation factor is also adapted so that the deformed model still can be considered as an animated head. Situations with defective scanned data are also discussed in this paper.

Quality Testing for Pressed Raised Character on Metal Label Using GRBF Networks

In accordance with the obvious characteristics of the pressed raised character image and the shortages of the template matching method.a new method of using the general radial-basis function neural network (GRBFN) for testing the quality of the pressed character is presented. The structures and training methods of GRBFN are fully analyzed, as well as the functionality of hidden layer, excited focus and area. The results show the checker based on GRBFN has highly checking ratio for the label pressed raised characters. It is suited to the quality testing of raised characters.

Subsurface drainage performance study using SALTMOD and ANN models

Relative performance of artificial neural networks (ANNs) and the conceptual model SALTMOD was studied in simulating subsurface drainage effluent and root zone soil salinity in the coastal rice fields of Andhra Pradesh, India. Three ANN models viz. Back Propagation Neural Network (BPNN), General Regression Neural Network (GRNN) and Radial Basis Function Neural Network (RBFNN) were developed for this purpose. Both the ANNs and the SALTMOD were calibrated and validated using the field data of 1998–2001 for 35 and 55 m drain spacing areas. Data on irrigation depth, evapotranspiration, drain discharges, water table depths, mean monthly rainfall and temperature and drainage effluent salinity were used for ANN model training, testing and validation. It was observed that the BPNN model with feed forward learning rule with 6 processing elements in input layer and 1 hidden layer with 12 processing elements performed better than the other ANN models in predicting the root zone soil salinity and drainage effluent salinity. Considering coefficient of determination, model efficiency and variation between the observed and predicted salinity values as the evaluation parameters, the SALTMOD performed better in predicting root zone soil salinity and the BPNN performed better in predicting the drainage effluent salinity. Therefore, it was concluded that the BPNN with feed forward learning algorithm was a better model than SALTMOD in predicting salinity of drainage effluent from salt affected subsurface drained rice fields.