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It is a crucial basis to improve the performance of neural network by constructing an appropriate activation function. This paper proposes a novel modulation window radial basis function neural network (MW-RBFNN) with an adjustable activation function. In this MW-RBFNN, a raised cosine radial basis function (RC-RBF) is adaptively modulated by an exponential function, and served as a shape-tunable activation function of MW-RBFNN. Compared with the basic RC-RBF neural network, the approximating ability of MW-RBFNN is improved due to its shape-tunable activation function. Besides, the computation of MW-RBFNN is far less than that of Gaussian radial basis function neural network (GRBFNN) because the MW-RBFNN is compactly supported. The training algorithm of MW-RBFNN is provided and its approximating ability is proved. Moreover, the regulation mechanism of the modulation index for the NN’s performance is proved and the regulating algorithm of the modulation index in MW-RBFNN is given. The computational complexity of MW-RBFNN is also analyzed. Five typical application cases are presented to illustrate the effectiveness of this proposed MW-RBFNN.

Deep neural networks (DNNs) can face limitations during training for recognition, motivating this study to improve recognition capabilities by optimizing deep learning features for hand gesture image recognition. We propose a novel approach that enhances features from well-trained DNNs using an improved radial basis function (RBF) neural network, targeting recognition within individual gesture categories. We achieve this by clustering images with a self-organizing map (SOM) network to identify optimal centers for RBF training. Our enhanced SOM, employing the Hassanat distance metric, outperforms the traditional K-Means method across a comparative analysis of various distance functions and the expanded number of cluster centers, accurately identifying hand gestures in images. Our training pipeline learns from hand gesture videos and static images, addressing the growing need for machines to interact with gestures. Despite challenges posed by gesture videos, such as sensitivity to hand pose sequences within a single gesture category and overlapping hand poses due to the high similarities and repetitions, our pipeline achieved significant enhancement without requiring time-related training data. We also improve the recognition of static hand pose images within the same category. Our work advances DNNs by integrating deep learning features and incorporating SOM for RBF training.

The hardware implementation of signal microprocessors based on superconducting technologies seems relevant for a number of niche tasks where performance and energy efficiency are critically important. In this paper, we consider the basic elements for superconducting neural networks on radial basis functions. We examine the static and dynamic activation functions of the proposed neuron. Special attention is paid to tuning the activation functions to a Gaussian form with relatively large amplitude. For the practical implementation of the required tunability, we proposed and investigated heterostructures designed for the implementation of adjustable inductors that consist of superconducting, ferromagnetic, and normal layers.

The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016 Stud. Appl. Math. 137, 174–188. (doi:10.1111/sapm.12106)). The method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set. This article generalizes this method to arbitrary smooth closed surfaces.

Botnet architectures are evolving rapidly, creating significant threats to global network security. This paper presents a homogeneous Radial Basis Function Neural Network (RBFNN) approach for botnet detection that employs a single, uniform RBFNN architecture with identical basis kernel types across all network components. Utilizing the CTU-13 dataset to extract flow-level packet length distribution features. These features are critical for identifying the distinct signatures of the 30 botnet types in the dataset, thereby enhancing the detection capabilities of our uniform RBF framework. The proposed model was designed to address the challenge of achieving high discriminative capability between Normal and Botnet activities while preserving the low latency needed for real-time deployment. Extensive experiments, including cross-validation and Operating Characteristic (ROC) analysis, show the model is effective, achieving a top classification accuracy of 98.31% and distinguishing well between Botnet and normal activities, with an Area Under the Curve (AUC) of 0.997. Furthermore, Training behavior analysis demonstrated stable convergence across different batch size configurations, highlighting trade-offs between accuracy and computational cost. A batch size of 64 provides an optimal balance between convergence speed and accuracy, with a total training time of 29.62 minutes. Crucially, the assessment of processing speed revealed a latency of 1.0118 microseconds. Such minimal delay validates the architecture’s suitability for high-speed network environments where real-time traffic analysis is imperative. Moreover, confusion matrix analysis further confirmed the reliability of the detection, with a low false-positive rate of nearly 0.018. Overall, the empirical results demonstrate that the homogeneous RBFNN offers an advanced solution for complex botnet detection.

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.

One of the most prevalent cancers that affects women is breast cancer. It ranks as the second most important factor in cancer-related deaths. The mortality rate can be decreased and survival rates raised with early detection and individualized risk assessment. The results of traditional risk prediction models, which are based on traditional risk factors, vary depending on the population. To solve these issues, this proposed system is designed. The dataset used for this analysis is the Mammogram Image Dataset. The Mammographic Image Analysis Society (MIAS) Digital Mammogram Database, which is publicly available, was used in this study. The study utilizes the MIAS in conjunction with Mini-Mammographic imaging datasets (Malignant, Benign, and Normal). The MIAS provided the 322 mammography images representing 161 individuals in the MIAS dataset. These images were taken at a resolution of 50 microns and included two mediolateral oblique (MLO) views. The system collects the digitized mammographic images as input. Then the raw data is pre-processed to remove unwanted data and noise. By using median filtering, important structural data is stored and maintains the mammogram image edges. The Fuzzy Clustering with Chicken Swarm Optimization (FC-CSO) technique will be classified into segments, and it separates suspicious regions like masses or calcifications from normal tissue. Based on labelling and annotation, the MIAS dataset determines whether the tissue is benign, malignant, or normal. The data from the labelling and annotation is given to feature extraction. The features of texture are essential for identifying the characteristics of tissue during this feature extraction process, which makes use of the Gray-Level Co-occurrence Matrix (GLCM). These characteristics are used to further classify the data. The data is then separated into testing sets and training sets. Seventy percent goes toward training, and thirty percent goes toward testing. The model is classified using Radial Basis Function Neural Networks (RBFNNs). By using radial basis functions as the activation functions in the hidden layer, this method enables the representation of complex patterns within the extracted feature space. RBFNN classifiers are then used to train the data into Normal, Benign, or Malignant categories. As a result, this system is used to accurately and early detect breast cancer. Therefore, An efficient automated mammogram breast cancer detection using Optimized Radial Basis Neural Network minimizes human error and processing time by combining FC-CSO for image segmentation, using a Gray-Level Co-occurrence Matrix for feature extraction, and using a RBFNN for data classification. Hence, this system shows better results in terms of accuracy, precision, specificity and processing time. The suggested FC-CSO–RBFNN technique outperforms current classifiers like SVM and XGBoost in terms of accuracy, precision, specificity, and computational time across mammography classification tasks.

In this paper, a new automated procedure based on deep learning methods for schizophrenia diagnosis is presented. To this aim, electroencephalogram signals obtained using a 32-channel helmet are prominently used to analyze high temporal resolution information from the brain. By these means, the data collected is employed to evaluate the class likelihoods using a neuronal network based on radial basis functions and a fuzzy means algorithm. The results obtained with real datasets validate the high accuracy of the proposed classification method. Thus, effectively characterizing the changes in EEG signals acquired from schizophrenia patients and healthy volunteers. More specifically, values of accuracy better than 93% has been obtained in the present research. Additionally, a comparative study with other approaches based on well-knows machine learning methods shows that the proposed method provides better results than recently proposed algorithms in schizophrenia detection. The proposed method can be used as a diagnostic tool in the detection of the schizophrenia, helping for early diagnosis and treatment.

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R2, and a comparison with another work is analyzed.