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Recently, the polynomial-based radial basis function neural networks (P-RBFNNs) have been successfully applied to regression tasks. However, the redundant and non-linear partitioned data easily interfere with accurate partitioning of clusters completed in P-RBFNNs, affecting the regression performance of this existing model. Because the squared error is used as the cost function of the learning method, P-RBFNNs are sensitive to noise interference. In order to cope with these problems, this study introduces a double iterative learning-based polynomial based-RBFNNs (DP-RBFNNs) modeling that focuses on the formation of architectures to improve the accuracy of regression performance as well as enhance the robustness through double iterative learning as follows: a) support vector-based Gaussian kernel fuzzy c-means (SV-GKFCM) as a kind of the support vector-based kernel fuzzy clustering are designed to determine connections (weights) between the input and hidden layers of the proposed model. SV-GKFCM helps effectively reduce the number of redundant data to re-modify the partitioning of clusters in the DP-RBFNNs. In addition, the cluster centers can be accurately updated from the non-linear partitioned data with the aid of Gaussian kernel distance in SV-GKFCM; b) least absolute shrinkage deviations (LASD) as a robust estimation are designed to update connection weights between the hidden and output layers. The SAE (sum of absolute error) function in the LASD method is used as a cost function to reduce the noise interference in the procedure of weight estimation as well as enhance the robustness of the DP-RBFNNs. The superiority of the proposed model is demonstrated through the experimental results. [ABSTRACT FROM AUTHOR]

Polynomial neural network (PNN) is a flexible self-organizing network model, and there have been lots of improvements to it. However, various and improved models of PNN do not properly balance their performance and efficiency. In this study, we present novel self-organized hybrid fuzzy neural networks (SHFNN). The purpose of this study is to develop a new design methodology of constructing a hybrid fuzzy model through enhanced input strategy (EIS) and probability-based node selection (PNS) to reinforce the performance of the model without sacrificing efficiency. l 2 -norm regularization (l 2) is utilized to mitigate overfitting as well as enhance generalization capability. The key points of SHFNN can be summarized as follows. First, a hybrid network structure is constructed by combining fuzzy radial basis function neural networks (FRBFNN) and PNN. Second, we propose a probability-based node selection strategy for node (neuron) selection. Third, an enhanced input strategy (EIS) is proposed to design the enhanced input set by merging the general candidate input set (GCIS) and the original candidate input set (OCIS). The regularization coefficient estimation method based on l 2 is used in conjunction with EIS and PNS to improve the performance and enhance the stability of the model. The effectiveness of SHFNN is validated using synthetic and machine learning dataset. The experimental results show that the prediction accuracy of the proposed model is improved by 4–22% when compared with some methods reported in the literature. Statistical analysis is also considered to demonstrate the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

• Overall structural framework designed for the restoration of motion-blurred images is proposed with the aid of PSO-based parameter estimation and image quality assessment. • The proposed Image Restoration Framework has a complete function which can effectively enhance the restored image quality. • Blur parameter estimation algorithm based on PSO (BPPO) is employed to optimize the motion-blurred parameter estimation. • A polynomial-based radial basis function neural network is used as image quality evaluation method to evaluate restored image quality for efficient classification. The restoration of motion-blurred images has always been a complex problem in image restoration. The current single blurred image algorithm cannot very well solve the estimation error of motion blur parameters. A comprehensive motion-blurred image restoration framework is proposed, which includes motion-blurred data generation, blur parameter estimation, and image quality assessment of restored images. First, we designed and used four image data sets with different degrees of blurring. We innovatively propose a blur parameter estimation algorithm based on the particle swarm optimization (B-PSO) algorithm. The Naturalness Image Quality Evaluator (NIQE) is used as the fitness function of the PSO algorithm. The framework also introduces a polynomial-based radial basis function neural network (P-RBFNN) as a new image quality assessment (IQA) method , with good image classification performance. Test results from public datasets show that the proposed framework can accurately estimate blur parameters. The peak signal-to-noise ratio (PSNR) reaches 29.976 dB, the structural similarity (SSIM) reaches 0.9044, and the classification rate is 96%. The proposed restoration framework produces the best image restoration results. [ABSTRACT FROM AUTHOR]

In this study, we propose a hybrid method of face recognition by using face region information extracted from the detected face region. In the preprocessing part, we develop a hybrid approach based on the Active Shape Model (ASM) and the Principal Component Analysis (PCA) algorithm. At this step, we use a CCD (Charge Coupled Device) camera to acquire a facial image by using AdaBoost and then Histogram Equalization (HE) is employed to improve the quality of the image. ASM extracts the face contour and image shape to produce a personal profile. Then we use a PCA method to reduce dimensionality of face images. In the recognition part, we consider the improved Radial Basis Function Neural Networks (RBF NNs) to identify a unique pattern associated with each person. The proposed RBF NN architecture consists of three functional modules realizing the condition phase, the conclusion phase, and the inference phase completed with the help of fuzzy rules coming in the standard ‘if-then’ format. In the formation of the condition part of the fuzzy rules, the input space is partitioned with the use of Fuzzy C-Means (FCM) clustering. In the conclusion part of the fuzzy rules, the connections (weights) of the RBF NNs are represented by four kinds of polynomials such as constant, linear, quadratic, and reduced quadratic. The values of the coefficients are determined by running a gradient descent method. The output of the RBF NNs model is obtained by running a fuzzy inference method. The essential design parameters of the network (including learning rate, momentum coefficient and fuzzification coefficient used by the FCM) are optimized by means of Differential Evolution (DE). The proposed P-RBF NNs (Polynomial based RBF NNs) are applied to facial recognition and its performance is quantified from the viewpoint of the output performance and recognition rate. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy modeling of complex systems is a challenging task, which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling. The IG-FRBFNN, a hybrid architecture of the IG-FIS (Fuzzy Inference System) and FRBFNN (Fuzzy Radial Basis Function Neural Networks), is proposed to address these problems. The paper is concerned with the analysis and design of IG-FRBFNNs and their optimization by means of the Hierarchical Fair Competition-based Parallel Genetic Algorithm (HFC-PGA). In the proposed network, the membership functions of the premise part of the fuzzy rules of the IG-based FRBFNN model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant, linear, quadratic and modified quadratic are considered for the consequent part of fuzzy rules. Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules. Since the performance of the IG-RBFNN model is affected by some key design parameters, such as a specific subset of input variables, the fuzzification coefficient of the FCM, the number of rules, and the order of polynomial of the consequent part of fuzzy rules, it becomes beneficial to carry out both structural as well as parametric optimization of the network. In this study, the HFC-PGA is used as a comprehensive optimization vehicle. The performance of the proposed model is illustrated by means of several representative numerical examples. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a new design methodology of fuzzy radial basis function-based polynomial neural networks. In many cases, these models do not come with capabilities to deal with granular information. With this regard, fuzzy sets offer several interesting and useful opportunities. This study presents the development of fuzzy radial basis function-based neural networks augmented with virtual input variables. The performance of the proposed category of models is quantified through a series of experiments, in which we use two machine learning data sets and two publicly available software development effort data. [Copyright &y& Elsevier]

Abstract: In this study, we design polynomial-based radial basis function neural networks (P-RBF NNs) based on a fuzzy inference mechanism. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient of the underlying clustering method) are optimized by means of the particle swarm optimization. The proposed P-RBF NNs dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy C-means (FCM). The network is of functional nature as the weights between the hidden layer and the output are some polynomials. The use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems. From the perspective of linguistic interpretation, the proposed network can be expressed as a collection of “if–then” fuzzy rules. The architecture of the networks discussed here embraces three functional modules reflecting the three phases of input–output mapping realized in rule-based architectures, namely condition formation, conclusion creation, and aggregation. The proposed classifier is applied to some synthetic and machine learning datasets, and its results are compared with those reported in the previous studies. [Copyright &y& Elsevier]

This study is concerned with the concept of Ensemble Fuzzy Radial Basis Function Neural Networks (EFRBFNN) endowed with clustering techniques, polynomial-based LSE/WLSE learning as well as their optimization implemented by Multi-Objective Particle Swarm Optimization (MOPSO). The network architecture of the proposed EFRBFNN classifier is considered three types of clustering techniques and four forms of regression polynomials. The proposed classifier can not only fully capture the local distribution (feature) information contained in the data, but also choose effective network architecture for improving classification performance and compactness. Three classes of clustering techniques (such as iterative self-organizing data analysis techniques algorithm (ISODATA), affinity propagation (AP), and extended K-means) are considered to effectively produce membership degrees based on feature information extraction suitable to fit data characteristics. Least Square Error Estimation (LSE) and Weighted Least Square Error Estimation (WLSE)-based learning with four types of regression polynomials are considered to estimate to coefficients of polynomials. MOPSO is exploited for choosing the effective architecture among different clustering techniques, polynomials, and polynomial-based learning with multi-objective parametric optimization. MOPSO helps achieve a sound compromise between the preferred classification performance and the compactness realized with the aid of four objective functions such as a) classification accuracy (CA), b) complexity of clustering, c) complexity of polynomial and d) sum of squared coefficients (SSC). The improvement and effectiveness of the proposed network architecture are quantified on a basis of the comprehensive experimental results and also a comparative analysis is offered to demonstrate the superiority of the proposed classifier. [ABSTRACT FROM AUTHOR]

Abstract: There is a remarkably rich landscape of fuzzy clustering and ensuing design procedures of information granules. In a nutshell, fuzzy clustering (and clustering, in general) leads to direction-free constructs meaning that there is no clear distinction between input and output variables. In the framework of fuzzy modeling, information granules are used in the development of input–output mapping and from this perspective it becomes beneficial to consider the aspect of directionality in the construction of information granules (fuzzy sets) in the input space. Conditional fuzzy C-means clustering comes as one of the algorithmically viable alternatives using which we construct fuzzy sets over the input space in presence of supervision coming in the form of structure of data distributed over the output space. In this paper, presented is a new clustering method in which we use the ambiguity index to express the boundaries of the clusters. The design is illustrated with the aid of several numeric examples that provide a detailed insight into the performance of the fuzzy models formed in this manner and also highlight several crucial design issues. [ABSTRACT FROM AUTHOR]