Abstract: Neural networks perform very well on difficult problems such as image or speech recognition as well as machine text translation. Classification based on fragmented and dispersed data representing certain properties of images or computer’s vision is a complex problem. Here, the suitability of a Radial Basis Function (RBF) neural network was evaluated using fragmented data in the problem of recognizing objects in images. The great difficulty of the considered problem is, there is not images data as such but only data on some properties of images stored in a dispersed form. More specifically, it was demonstrated that applying a $$k-$$ nearest neighbors classifier in the first step to generate predictions based on fragmented data, and then using a RBF neural network to learn how to correctly recognize the systems of generated predictions for making a final classification is a good approach for recognizing objects in images. An additional step of training the weights (centers) between the input and hidden layers of a RBF network was proposed. In general, this investigation demonstrates that adding this step significantly improves the correctness of recognizing objects in images.

Abstract: The radial basis function neural network (RBFNN) is a widely used tool for interpolation and prediction problems. In this paper, we propose to improve the traditional RBFNN by automatically identifying core neurons in the hidden layer, based on the [Formula: see text] regularization. Our proposed approach will greatly reduce the number of neurons required, which will save the memory and also the computational cost. To determine the radial parameter [Formula: see text] in the RBFs, we propose to use the [Formula: see text]-fold cross-validation method. Moreover, the principal component analysis (PCA) method is used to reconstruct the distance between samples for high-dimensional data sets. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.

Abstract: The radial basis function (RBF) neural network is a type of universal approximator, and has been widely used in various fields. Improving the training speed and compactness of RBF networks are critical for promoting their applications. In the present study, we propose a simple, fast, and effective RBF networks training method, which is based on the residual extreme points and their neighborhoods (thus called the REN method for short in this paper). The REN method calculates RBF centers and widths through a two-level iterative process, and realizes two main functionalities, namely 1) adding multiple centers within one pass through the whole data set, and 2) calculating RBF widths specifically for each center. The use of this algorithm does not need any parameter adjustments, and the models for approximation or classification can be obtained by only one run. The performance of the proposed REN algorithm is compared with the classic and powerful orthogonal least squares (OLS) algorithm. By reaching the same accuracies, the REN algorithm trains RBF networks 50 and 320 times faster, in the chirp (0˜50 Hz, 2 s, 1 kHz, 2001 samples) and two-dimensional peaks (2401 samples) signal approximation tasks respectively, than the OLS algorithm does, and the number of centers obtained by the REN algorithm is reduced by half. When incorporating the same number of centers, the REN algorithm achieves accuracies up to 3 orders of magnitude higher than the best results obtained by the OLS algorithm. In the classification task of a real discrete breast cancer data, both methods result in accuracies comparable to many existent methods, but the REN algorithm has the advantages of fast training speeds and no requirements for parameter adjustments. The REN algorithm proposed in this study may potentially be used for tasks with large scale of data or applications that require high model performances.

Abstract: Early detection of cardiac arrhythmia is of great importance both for the patients and the cardiologist for proper treatment. The detection is achieved through an extensive analysis of the electrocardiogram (ECG) signals, feature extraction method and machine learning techniques. The extracted features are used for the classification of the different types of arrhythmias. This research presents sequential feature selection (SFS) method whereas, the extracted features are fed into the classifiers; the Fuzzy Neural Network (FNN), Naïve Bayes (NB) and Radial Basis Function Network (RBFN) for classification. Observations from the results demonstrated that FNN gained the highest accuracy of 99% as compared with the other two machine learning techniques; NB and RBFN.

Abstract: : Finding plant leaves is a crucial step in preventing a major outbreak. The automatic diagnosis of plant disease is an important research area. Similar to humans and other animals, plants also experience the negative effects of sickness. These diseases affect the entire plant, including the leaf, stem, fruit, root, and flower. More often than not, when a plant's sickness is left untreated, the plant bites the ground or can also cause the loss of leaves, blooms, natural products, and so forth. For accurate identification and treatment of plant diseases, these disorders must be properly dedicated. The study of plant infections, their causes, and methods for containing and managing them is known as plant pathology. However, the modern strategy emphasises human inclusion for order and differentiating disease evidence. This strategy is time-consuming and expensive. Programmable disease detection from plant leaf images using a sensitive registration technique may be more valuable than the existing one. In this research, we present a method for identifying symptoms and characterising plant leaf illnesses organically called Bacterial looking development based entirely Radial Basis Function Neural Network (BRBFNN). We employ bacterial looking streamlining (BFO), which also increases the speed and accuracy of the device, to give Radial Basis Function Neural Network (RBFNN) the best possible weight when understanding various illnesses at the plant Leaf's. The suggested method improves recognition of evidence and infection characterisation.

Abstract: This study used the salp swarm algorithm (SSA), Henry gas solubility optimization algorithm (HGSOA), and crow optimization algorithm (COA) to adjust the radial basis function neural network (RABFN) parameters for predicting monthly rainfall. Then, a new ensemble model was created using the outputs of RABFN, RABFN-SSA, RABFN-HGSOA, and RABFN-COA. The new ensemble model was named inclusive multiple model (IMM). This study indicated that the ensemble models improved the efficiency of the optimized RABFN models. The training MAE of the IMM, RABFN-HGSOA, RABFN-SSA, RABFN-PSO, and RBFN models was 0.987, 1.35, 1.47, 1.58, and 2.21 mm. The IMM reduced the testing MAE of the IMM, RABFN-HGSOA, RABFN-SSA, RABFN-PSO, and RBFN models by 32%, 37%, 42%, and 55%, respectively. Also, the HGSOA had better performance than the SSA and COA.

Abstract: An extension of radial basis functions in numerical analysis, radial basis function networks (RBFN) are used to model dehumidifying coils and compared with multilayer perceptron networks (MLPN). A method similar to backpropagation is used to train the network in a supervised fashion. During the training of the network, all parameters are updated to minimize the difference between the desired outputs and outputs of the network response to the corresponding input vector.

Abstract: Extreme Learning Machine (ELM) is a feed-forward neural network with one hidden layer. In its modification called ELM Radial Basis Function the input data is a priori clustered into a number of sets represented by their centroids. The matrix of distances between each sample and centroid is calculated and applied as input data to the neural network. This work conducts a comparison study of the ELM Radial Basis Function classification performance upon applying either k-means, k-medoids or mean shift clustering methods. Generated results are obtained from two datasets i.e. Wine Quality-White and Ionosphere. The computations are based on full datasets or on the same both sets reduced by a feature selection algorithm. The parameters of the classifiers such as number of neurons in hidden layer, the value of k in k-means and k-medoids, the value of radius in mean shift are optimized through an iterative procedure upon maximizing an accuracy or minimizing Mean Square Error and computation time. The different distance metrics for k-means and k-medoids, and mean shift with Gaussian or flat kernel function are also compared. The results obtained with Softplus and linear activation function (applied in most of the computations in this work) are juxtaposed with the results generated by other activation functions.

Abstract: This paper proposes an efficient method for wind power generation output forecasting. The proposed method is based on Radial Basis Function Network (RBFN) of Artificial Neural Network (ANN). In this paper, a couple of strategies are proposed to improve the performance of RBFN. One is the use of the Wavelet Transform as the preconditioning technique while the other is to apply the idea of ELM (Extreme Learning Machine) to RBFN. The effectiveness of the proposed method is demonstrated for real data of wind power generation output.

Abstract: In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the $d$-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.

Abstract: The wear reliability analysis model of pantograph systems is built based on a radial basis function neural network in this paper, complicated and strong nonlinear wear characteristics of pantograph systems are obtained, and the wear variational laws with external parameters are analyzed. By Comparing the optimized radial basis function neural network performance in relative errors and learning speed with BP neural network and ordinary radial basis function neural network, the optimized radial basis function neural network has strong ability of nonlinear mapping and functional approach, and obtains high prediction accuracy. The study provides a simple and feasible method for wear characteristic analysis and wear reliability design of pantograph systems in electric railroad.

Abstract: Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs) with multiscale coefficients. Inspired by the deep mixed residual method, we rewrite the second-order problem into a first-order system and employ multiple radial basis function neural networks (RBFNNs) to approximate unknown functions in the system. To aviod the overfitting due to the simplicity of RBFNN, an additional regularization is introduced in the loss function. Thus the loss function contains two parts: the $L_2$ loss for the residual of the first-order system and boundary conditions, and the $\ell_1$ regularization term for the weights of radial basis functions (RBFs). An algorithm for optimizing the specific loss function is introduced to accelerate the training process. The accuracy and effectiveness of the proposed method are demonstrated through a collection of multiscale problems with scale separation, discontinuity and multiple scales from one to three dimensions. Notably, the $\ell_1$ regularization can achieve the goal of representing the solution by fewer RBFs. As a consequence, the total number of RBFs scales like $\mathcal{O}(\varepsilon^{-nτ})$, where $\varepsilon$ is the smallest scale, $n$ is the dimensionality, and $τ$ is typically smaller than $1$. It is worth mentioning that the proposed method not only has the numerical convergence and thus provides a reliable numerical solution in three dimensions when a classical method is typically not affordable, but also outperforms most other available machine learning methods in terms of accuracy and robustness.

Abstract: This work focuses on radial basis functions containing no parameters with the main objective being to comparatively explore more of their effectiveness. For this, a total of sixteen forms of shapeless radial basis functions are gathered and investigated under the context of the pattern recognition problem through the structure of radial basis function neural networks, with the use of the Representational Capability (RC) algorithm. Different sizes of datasets are disturbed with noise before being imported into the algorithm as ‘training/testing’ datasets. Each shapeless radial basis function is monitored carefully with effectiveness criteria including accuracy, condition number (of the interpolation matrix), CPU time, CPU-storage requirement, underfitting and overfitting aspects, and the number of centres being generated. For the sake of comparison, the well-known Multiquadric-radial basis function is included as a representative of shape-contained radial basis functions. The numerical results have revealed that some forms of shapeless radial basis functions show good potential and are even better than Multiquadric itself indicating strongly that the future use of radial basis function may no longer face the pain of choosing a proper shape when shapeless forms may be equally (or even better) effective.