Search

Determining the right number of clusters without any prior information about their numbers is a core problem in cluster analysis. In this paper, we propose a nonparametric clustering method based on different weighted spatial rank (WSR) functions. The main idea behind WSR is to define a dissimilarity measure locally based on a localized version of multivariate ranks. We consider a nonparametric Gaussian kernel weights function. We compare the performance of the method with other standard techniques and assess its misclassification rate. The method is completely data-driven, robust against distributional assumptions, and accurate for the purpose of intuitive visualization and can be used both to determine the number of clusters and assign each observation to its cluster. [ABSTRACT FROM AUTHOR]

In economics, we know the law of demand: a higher price will lead to a lower quantity demanded. The question is to know how much lower the quantity demanded will be. Similarly, the law of supply shows that a higher price will lead to a higher quantity supplied. Another question is to know how much higher. To find answers to these questions which are critically important in the real world, we need the concept of elasticity. Elasticity is an economics concept that measures the responsiveness of one variable to changes in another variable. Elasticity is a function e x that can be built from an arbitrary function y = g x . Elasticity at a certain point is usually calculated as e x = d y / d x x / y . Elasticity can be expressed in many forms. An interesting form, from an economic point of view, is the ratio between the derivative of the logarithm of the distribution function with respect to the logarithm of the point x , which is developed in this article. The aim of this article is to study the direction of variation of this elasticity function and to construct a nonparametric estimator because the estimators that have been constructed so far are parametric estimators and admit many deficiencies in practice. And finally, we study the strong consistency of the said estimator. A numerical study was carried out to verify the adequacy of the theory. [ABSTRACT FROM AUTHOR]

This study discusses the practical engineering problem of determining random load sources on coal-rock structures. A novel combined regularization technique combining mollification method (MM) and discrete regularization (DR), which was called MM-DR technique, was proposed to reconstruct random load sources on coal-rock structures. MM-DR technology is compared with DR, Tikhonov regularization (TR), and maximum entropy regularization (MER) in load reconstruction. The results show that the reconstructed random load sources are more consistent with the real load sources using MM-DR technique combined with particle swarm optimization (PSO) and L-curve method, which was named as PSO-L method, and selecting optimal ω value of kernel function is beneficial to overcome the ill-posed of random load sources reconstruction and to obtain the stable and approximate solutions. The method proposed in this study provides a theoretical basis for the recognition of coal-rock interface. [ABSTRACT FROM AUTHOR]

Accurate and reliable traffic state identification is the prerequisite for developing intelligent traffic programs. With the improvement of intelligent traffic control measures, the traffic state of some highways has gradually stabilized. The current research on traffic state identification needs to fully meet the highly informative intelligent traffic system and traffic state subcategory analysis. To fill the gap above, we propose an improved support tensor machine (STM) method based on self-training and multiclassification for traffic state subcategory identification (ISTM) with ETC gantry data. This paper takes the excellent application of the support vector machine (SVM) in traffic state identification as the starting point of method design and extends to the STM. The ETC gantry data are represented as a third-order tensor model. This paper utilizes the similarity among tensor samples to construct the kernel function and recognize the traffic states. We simplify STM calculation with a one-against-one model and a self-training idea. An optimal fit of the characteristics is supplied by maximizing inter-subcategory tensor block distances and minimizing intra-subcategory tensor block distances throughout a joint utilization of the STM and multiscale training theories. The experiment in this paper uses ETC gantry data from the Jingtai highway in Shandong Province, and the findings reveal that the ISTM has optimum values of 0.2578 and 0.3254 for the SumD and 0.1718 and 0.1901 for the DBI as compared to K-mean clustering and the SVM. The ISTM trains the traffic state subcategory classifiers with high accuracy and strong generalization ability. [ABSTRACT FROM AUTHOR]

Multikernel clustering achieves clustering of linearly inseparable data by applying a kernel method to samples in multiple views. A localized SimpleMKKM (LI-SimpleMKKM) algorithm has recently been proposed to perform min-max optimization in multikernel clustering where each instance is only required to be aligned with a certain proportion of the relatively close samples. The method has improved the reliability of clustering by focusing on the more closely paired samples and dropping the more distant ones. Although LI-SimpleMKKM achieves remarkable success in a wide range of applications, the method keeps the sum of the kernel weights unchanged. Thus, it restricts kernel weights and does not consider the correlation between the kernel matrices, especially between paired instances. To overcome such limitations, we propose adding a matrix-induced regularization to localized SimpleMKKM (LI-SimpleMKKM-MR). Our approach addresses the kernel weight restrictions with the regularization term and enhances the complementarity between base kernels. Thus, it does not limit kernel weights and fully considers the correlation between paired instances. Extensive experiments on several publicly available multikernel datasets show that our method performs better than its counterparts. [ABSTRACT FROM AUTHOR]

The uniaxial compression experiment of red sandstone is observed simultaneously by using acoustic emission and digital speckle correlation methods. The deformation evolution of red sandstone is divided into microfracture random expansion stage, deformation localization stage, subinstability stage, and instability failure stage. Green's function and dispersion curve of each stage are obtained from the noise data picked up by acoustic emission equipment, and the dispersion characteristics of each evolution stage are analyzed. The results show the following: (1) In the stage of random propagation of microcracks, the noise in the low frequency range passes through at a higher phase velocity, the phase velocity changes periodically, the correlation coefficient is high at the initial time, and the variation trend of frequency dispersion curve is relatively consistent. (2) In the deformation localization stage, the frequency range without zero phase velocity moves to the high frequency range, and the phase velocity changes periodically. (3) In the subinstability stage, dense phase velocity zeros appear on the dispersion curve image, the dispersion curve tends to be disordered, various indicators change obviously, and the correlation coefficient decreases rapidly. (4) In the unstable failure stage, the fracture evolution is completed, and the variation trend of each index of the frequency dispersion curve is consistent. (5) The size and difference of the sensitive kernel function of the two layers are related to the evolution region of the fracture. The sensitivity kernel value of the medium layer where the fracture evolves is high, and the longer the evolution time, the greater the difference. [ABSTRACT FROM AUTHOR]

The convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around 1 in the training process. We propose a new Frobenius norm penalty function for a convolutional kernel tensor to let the singular values of the corresponding transformation matrix be bounded around 1. We show how to carry out the gradient-type methods. This provides a potentially useful regularization method for the weights of convolutional layers. [ABSTRACT FROM AUTHOR]

The convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around 1 in the training process. We propose a new Frobenius norm penalty function for a convolutional kernel tensor to let the singular values of the corresponding transformation matrix be bounded around 1. We show how to carry out the gradient-type methods. This provides a potentially useful regularization method for the weights of convolutional layers. [ABSTRACT FROM AUTHOR]

In most cases, the blasting object is the rock mass. Because the rock mass has the characteristics of anisotropy and inhomogeneity, there are often structural surfaces such as joints, fissures, faults, and weak interlayers, but details are basically impossible. Compared with the rock, these structural surfaces are weak parts, and the explosive energy required for breaking is smaller. It is difficult to take into account the existence of each weak side when the explosives are arranged in the blasthole. Therefore, after the explosive explodes in the rock mass, the explosive gas will first rush out from these weak parts, entraining individual fragments to form flying rocks. Aiming at the problem that it is difficult to accurately obtain the rock motion information in the blasting process of open-pit mines, this paper selects the kernel function to establish the support vector machine model and optimizes the parameters of the support vector machine model to obtain the optimal blasting rock trajectory prediction model. Under the protection of special protection devices, the information of the rock movement during the blasting process is collected at a higher frequency, and the analysis algorithm of the rock movement characteristics is researched on the basis of inertial navigation technology. The algorithm is used to analyze and output the rock movement. The curve of velocity, position, and kinetic energy provides a theoretical and technical basis for the study of rock movement law in the blasting process of open-pit mines. Through the experimental analysis, based on the cross-validation method, through the support vector machine model parameter optimization and comparison evaluation parameters, the optimal prediction model of the blasting rock trajectory is obtained as the support vector machine model based on the radial basis kernel function. The mean value of root mean square error and mean absolute error of this model are 0.102 and 0.0674, respectively, and the performance is the most robust among the three types of models. [ABSTRACT FROM AUTHOR]

Piano score recognition is one of the important research contents in the field of music information retrieval, and it plays an important role in information processing. In order to reduce the influence of vocals on the progress of piano notes and restore the harmonic information corresponding to piano notes, the article models the harmonic information and vocal information corresponding to piano notes in the frequency spectrum. We use the phase space reconstruction method to extract the nonlinear feature parameters in the note audio and use some of the parameters as the training set to construct the support vector machine (SVM) classifier and the other part as the test set to test the recognition effect. Therefore, the method of adaptive signal decomposition and SVM is introduced into the signal preprocessing link, and the corresponding recognition process is established. In order to improve the performance of the support vector machine, the article uses measurement learning method to obtain the measurement learning and uses the measurement learning to replace the Euclidean distance of the Gaussian kernel function of the support vector machine. The SVM method of adaptive signal decomposition and the SVM method of principal component analysis are introduced into the preprocessing process of the note signal, and then the preprocessed signal is reconstructed in phase space, and the corresponding recognition process is established. The method of directly reconstructing the phase space of the original signal has higher accuracy and can be applied to the note recognition of continuous music segments. The final experimental results show that, compared with the current popular piano score recognition algorithm, the recognition accuracy of the proposed piano score recognition algorithm is improved by 3.5% to 12.2%. [ABSTRACT FROM AUTHOR]

Fog-assisted and IoT-enabled smart healthcare system with rapid response rates is the major area of concern now a days. Dynamic and heterogeneous fog networks are difficult to manage and a considerable amount of overhead could be realized while managing ever increasing load on foglets. Fog computing plays a vital role in managing ever increasing processing demands from diverse IoT-based applications. Smart healthcare systems work with the assistance of sensor-based devices and automatic data collection and processing can speed up overall system functionality. In the proposed work, a novel framework for smart health care is presented where a series of activities are performed with prime objective of reducing latency and execution time. Principal component analysis is used for feature reduction and support vector machines with radial basis function kernel is used for classification purpose. Workload optimization on the fog nodes is implemented using genetic algorithm. Data collection process also involves preprocessing as a leading step for generating cleaner data. Amalgamation of intelligent and optimization techniques in the presented framework certainly improves the efficiency of the overall system. Experimental results reveal that proposed work outperforms the existing fog-assisted smart healthcare systems in terms of latency, execution time, overall system accuracy, and system stability. [ABSTRACT FROM AUTHOR]

Nuclear methods, such as the study of the main components of nuclear and the support of vector machines, have gradually evolved into a type of pillar methods for pattern recognition and economic statistics. Therefore, how to choose the inner product function of high-dimensional space is particularly important for the use of such methods. And, because the inner product function of high-dimensional space often determines the structure of high-dimensional space, the superiority of the kernel method is directly affected by using high-dimensional space. Due to its superior performance, the inner product function of Gaussian high-dimensional space has been put into practical use to a large extent. For the processing of unbalanced distribution of BGP data, because the results of BGP usually have multiple results, and the distribution is not uniform, so in the process of training SVM, the process of determining the composition of the hyperplane is generated due to various results The effect of the results will also be different so that the final planning equation has errors and weakens the classification ability. Finally, the BGP test results are displayed. The results show that the operation of the SVM algorithm can complete the supervision and management of BGP abnormal data. If there is any data fluctuation, an alarm will be issued. Under the condition of ensuring the correct rate, the input characteristics of BGP can be reduced in dimensionality, and specific selection methods can be used to complete. A high-level algorithm is used here, so that it has a better SVM classification effect, and abnormal traffic can be more conveniently and quickly checked out of BGP. It can be seen from the results of statistical analysis of urban and rural data that the current gap between urban and rural economic development level is too large, and to some extent, there is a trend of increasing fault, which will undoubtedly affect the stability of urban and rural areas, so the urban-rural income gap should be narrowed. We have also studied the principle of the general preferential economy in rural areas and put forward relevant effective strategy. [ABSTRACT FROM AUTHOR]

The prediction of casualties in earthquakes is very important for improving the efficiency of emergency rescue measures and reducing the number of casualties. Given the time lag and poor accuracy of population density data published in statistical yearbooks, a Baidu heatmap is used in this study to accurately estimate the regional population density. Based on the standard support vector machine (SVM) prediction model, a piecewise loss function and a robust wavelet kernel function are proposed to effectively reduce the prediction error. Given a characteristic attribute set of factors related to earthquake casualties, the new prediction model is tested in 34 cases involving earthquake cases on the Chinese mainland since 2011. Compared with other prediction techniques, the proposed robust wavelet SVM can converge more quickly, and the prediction error is lower than that of the standard backpropagation neural network (BPNN) and standard SVM. [ABSTRACT FROM AUTHOR]

The convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around 1 in the training process. We propose a new Frobenius norm penalty function for a convolutional kernel tensor to let the singular values of the corresponding transformation matrix be bounded around 1. We show how to carry out the gradient-type methods. This provides a potentially useful regularization method for the weights of convolutional layers. [ABSTRACT FROM AUTHOR]

Cluster analysis plays a very important role in the field of unsupervised learning. The multikernel function is used to transform the low-dimensional nonlinear relationship of the influencing factors of consumption behavior into a high-dimensional linear problem, thereby improving the aggregation ability of clustering for multidimensional spatial data. In this study, a multikernel fuzzy clustering method is proposed to handle sporting consumption behavior problems. In the clustering process, the weight coefficients of different kernel functions are automatically adjusted based on fuzzy criteria to improve the feature learning ability of the combined kernel function and the generalization ability of the system after clustering. Extensive experimental results show the promising performance of the proposed multikernel clustering method. [ABSTRACT FROM AUTHOR]

Summary: Lithium‐ion batteries are used in a wide range of applications due to their cleanliness and stability, and the health management of lithium‐ion batteries has become a necessity. The most important aspect of health management is the prediction of the remaining useful life (RUL) of the battery. Therefore, a RUL estimation model based on the aging factor of the charging process and an improved multi‐kernel relevance vector machine is proposed in order to achieve high accuracy estimation of the RUL of lithium‐ion batteries. First, eight aging features highly correlated with lithium‐ion batteries capacity degradation are extracted based on charging current, voltage, and temperature data, then, their correlation is proved using gray relation analysis. Secondly, the improved gray wolf constrained optimization algorithm is used to determine the kernel function combination coefficients of the multi‐kernel relevance vector machine, and the RUL prediction model of the improved multi‐kernel relevance vector machine is established. Finally, using the battery dataset from NASA, aging data of three datasets, 24°C, 43°C, and 4°C, with a total of 11 batteries, were selected for validation. The validation results show that the improved multi‐kernel relevance vector machine prediction model has higher prediction accuracy and more robust long‐term prediction capability, with RUL prediction error less than 10 cycles and MAE less than 0.05, both of which are better than that of the single‐kernel relevance vector machine model and other multi‐kernel relevance vector machine models. [ABSTRACT FROM AUTHOR]

This paper proposes a fuzzy combined kernel relevance vector machine method for the coal spontaneous combustion temperature prediction to avoid the shortcomings of traditional machine learning algorithms, such as the large prediction error, the weak generalization ability of the single kernel function, and the inability to deal with abnormal values. First, build a platform to simulate the coal spontaneous combustion scene and obtain the data of different index gas concentrations and the coal spontaneous combustion temperature through experiments. Second, the fuzzy algorithm is used to give the training samples different membership degrees with attention, so as to reduce the influence of outliers on the model. Third, the combined kernel function weighted by the polynomial kernel function and Gaussian kernel function is used to construct the input sample matrix to map the data from the low-dimensional space to a high-dimensional space, so as to obtain a better training model. Finally, the fuzzy combined kernel relevance vector machine model is constructed and compared with methods based on the radial basis function neural network, least squares support vector machine, Gaussian kernel relevance vector machine, and combined kernel relevance vector machine to verify the effectiveness of prediction for coal spontaneous combustion temperature. The results show that the fuzzy combined kernel relevance vector machine not only has the characteristics of strong generalization ability and weakening the influence of abnormal data, but also with a more sparse model, which is suitable for the prediction of coal spontaneous combustion temperature. [ABSTRACT FROM AUTHOR]

Dyslexia is among the most common neurological disorders in children. Detection of dyslexia therefore remains an important pursuit for the research works across various domains which is illustrated by the plethora of work presented in diverse scientific articles. The work presented herein attempted to utilize the potential of a unified gaming test of subjects (dyslexia/controls) in tandem with principal components derived from data to detect dyslexia. The work aims to build a machine learning model for dyslexia detection using comprehensive gaming test data. We have attempted to explore the potential of various kernel functions of the Support Vector Machine (SVM) on different number of principal components to reduce the computational complexity. A detection accuracy of 92% is obtained from the radial basis function with 5 components, and the highest detection accuracy obtained from the radial basis function with 3 components is 93%. On the contrary, the Artificial Neural Network(ANN) shows an added advantage with minimal number of hyperparameters with 3 components for obtaining an accuracy of 95%. The comparison of the proposed method with some of the existing works shows efficacy of this method for dyslexia detection. [ABSTRACT FROM AUTHOR]

In recent years, the interdisciplinary exploration of combining traditional visual communication design with somatosensory interaction technology has become a new form of artistic expression. In order to explore the feasibility of somatosensory interaction technology in visual communication design, this study proposes a 2D dynamic graphic generation method based on somatosensory interaction parameterisation and uses traditional Chinese elements as an example for specific applications in visual communication design. Firstly, the motion parameters recognised using the Kinect somatosensory interaction device are bound to the function variables used to generate the images in the development environment, thus enabling human somatosensory interaction with different characters in the scene. Secondly, a linear discriminant analysis based on kernel functions is used to reduce the dimensionality of the vector space, thus solving the problem of real-time and accurate capture of human movements. Then, using the skeletal parameter binding technique, the association between the motion parameters of the somatosensory interaction and the two-dimensional dynamic graphics is achieved. The experimental results show that the visual communication technique based on somatosensory interaction has a high recognition accuracy. Distinguished from traditional digital video, the proposed method can greatly enrich the visual representation of traditional Chinese elements. [ABSTRACT FROM AUTHOR]

Alzheimer's disease is the neuro disorder which characterized by means of Amyloid– β (A β) in brain. However, accurate detection of this disease is a challenging task since the pathological issues of brain are complex in identification. In this paper, the changes associated with the retinal imaging for Alzheimer's disease are classified into two classes such as wild-type (WT) and transgenic mice model (TMM). For testing, optical coherence tomography (OCT) images are used to classify into two groups. The classification is implemented by support vector machines with the optimum kernel selection using a genetic algorithm. Among several kernel functions of SVM, the radial basis kernel function provides the better classification result. In order to deal with an effective classification using SVM, texture features of retinal images are extracted and selected. The overall accuracy reached 92% and 91% of precision for the classification of transgenic mice. [ABSTRACT FROM AUTHOR]

Seismic demand analysis of structures plays an important role in the structural seismic calculation; however, studies on the importance analysis of seismic demand are limited. A new method based on a support vector machine (SVM) is proposed to analyze the importance of structural seismic demand and study the influence of random variables on structural seismic demand in this study, where the linear kernel function, Gauss kernel function, and polynomial kernel function are used in SVM. The time history analysis of the steel-reinforced concrete (SRC) frame structures has been carried out by the finite element software OpenSees under the action of different seismic records. Four kinds of seismic demand of the SRC frame structure are analyzed in this study, which are top displacement, maximum floor acceleration, base shear, and maximum interstory drift angle, respectively. Importance indexes of the four kinds of structural seismic demand are in good agreement with those of the Monte Carlo (MC) numerical simulation method and Tornado graphic method, which verify the accuracy of the proposed method. Moreover, the sample size of the proposed method is greatly smaller than that of the MC method. Therefore, the computation efficiency has been improved significantly by the proposed method. [ABSTRACT FROM AUTHOR]

Thermal conductivity (TC) of a phase change material (PCM) may be enhanced by distributing nanostructured materials (NSMs) termed nano-PCM. It is critical to accurately estimate the TC of nano-PCM to assess heat transfer during phase transition processes, namely, solidification and melting. Here, we propose Gaussian process regression (GPR) strategies involving four various kernel functions (KFs) (including exponential (E), squared exponential (SE), rational quadratic (RQ), and matern (M)) to predict TC of n-octadecane as a PCM. The accessible computational techniques indicate the accuracy of our proposed GPR model compared to the previously proposed methods. In this research, the foremost forecasting strategy has been considered as a GPR method. This model consists of the matern KF whose R2 values of training and testing phases are 1 and 1, respectively. In the following, a sensitivity analysis (SA) is used to explore the effectiveness of variables in terms of outputs and shows that the temperature (T) of nanofluid (NF) is the most efficient input parameter. The work describes the physical properties of NFs and the parameters that should be determined to optimize their efficiency. [ABSTRACT FROM AUTHOR]

This work aims to develop a robust machine learning model for the prediction of the relative viscosity of nanoparticles (NPs) including Al2O3, TiO2, SiO2, CuO, SiC, and Ag based on the most important input parameters affecting them covering the size, concentration, thickness of the interfacial layer, and intensive properties of NPs. In order to develop a comprehensive artificial intelligence model in this study, sixty-nine data samples were collected. To this end, the Gaussian process regression approach with four basic function kernels (Matern, squared exponential, exponential, and rational quadratic) was exploited. It was found that Matern outperformed other models with R2 = 0.987, MARE (%) = 6.048, RMSE = 0.0577, and STD = 0.0574. This precise yet simple model can be a good alternative to the complex thermodynamic, mathematical-analytical models of the past. [ABSTRACT FROM AUTHOR]

Nowadays, fractional derivative is used to model various problems in science and engineering. In this paper, a new numerical method to approximate the generalized Hattaf fractional derivative involving a nonsingular kernel is proposed. This derivative included several forms existing in the literature such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. The new proposed method is based on Lagrange polynomial interpolation, and it is applied to solve linear and nonlinear fractional differential equations (FDEs). In addition, the error made during the approximation of the FDEs using our proposed method is analyzed. By comparing the approximate and exact solutions, it is noticed that the new numerical method is very efficient and converges very quickly to the exact solution. Furthermore, our proposed numerical method is also applied to nonlinear systems of FDEs in virology. [ABSTRACT FROM AUTHOR]

In this paper, we define the space of functions Λ p -bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, Λ p B V I a b , ℝ . [ABSTRACT FROM AUTHOR]

The fractional integral inequalities are crucial to deal applied problems. The present paper deals with the generalize midpoint type inequalities for a certain class of convex functions, namely, MT-convex functions in the setting of weighted fractional integral. It can be observed from the remarks given in the paper that our results or more generalized than existing results of literature and many of them can be obtained immediately from our results. [ABSTRACT FROM AUTHOR]

As in parametric regression, nonparametric kernel regression is essential for examining the relationship between response variables and covariates. In both methods, outliers may affect the estimators, and hence robustness is essential to deal with practical issues. This paper proposes a family of robust nonparametric estimators with unknown scale parameters for regression function based on the kernel method. In addition, we establish the asymptotic normality of the estimator under the concentration properties on small balls of probability measure of the functional explanatory variables. The superiority of the proposed methods is shown through numerical and real data studies to compare the sensitivity to outliers between the classical and robust regression (fixed and unknown scale parameter). Such a new proposed method will be useful in the future for analyzing data and making decisions. [ABSTRACT FROM AUTHOR]

Wireless sensor network is an ad hoc network with sensing capability. Usually, a large number of sensor nodes are randomly deployed in an unreachable environment or complex area for data collection and transmission, which can realize the perception and monitoring of the target area or specific objects and transmit the obtained data to the remote end of the system. Human health activity recognition algorithm is a hot topic in the field of computer. Based on the small sample problem and the linear indivisibility of real samples encountered in metric learning, this paper proposes a human activity recognition algorithm for wireless sensor networks. Human activity recognition algorithm for wireless sensor networks uses human activity recognition algorithm to solve the singularity of intraclass divergence matrix, so as to reduce the impact of small sample problem. The algorithm maps two different feature spaces to the high-dimensional linearly separable kernel space through the corresponding kernel function, calculates the distance between samples in the two projected feature subspaces to obtain two distance measurement functions, and finally linearly combines them with weights to obtain the final distance measurement function. [ABSTRACT FROM AUTHOR]

The Szegö kernel has many applications to problems in conformal mapping and satisfies the Kerzman-Stein integral equation. The Szegö kernel for an annulus can be expressed as a bilateral series and has a unique zero. In this paper, we show how to represent the Szegö kernel for an annulus as a basic bilateral series (also known as q -bilateral series). This leads to an infinite product representation through the application of Ramanujan's sum. The infinite product clearly exhibits the unique zero of the Szegö kernel for an annulus. Its connection with the basic gamma function and modified Jacobi theta function is also presented. The results are extended to the Szegö kernel for general annulus and weighted Szegö kernel. Numerical comparisons on computing the Szegö kernel for an annulus based on the Kerzman-Stein integral equation, the bilateral series, and the infinite product are also presented. [ABSTRACT FROM AUTHOR]

In the process of extracting the characteristic frequency of the fault signal of the rolling bearing in the mechanical system, the signal transmission paths between the fault points inside the bearing and the sensor are diversified, which will produce compound faults of different forms and combinations. These composite faults will lead to a series of serious consequences such as distortion and aliasing of the fault characteristic spectrum. In order to solve these problems, this paper proposes a composite fault feature separation method for rolling bearing based on the mixed function decoupling model. Firstly, the functional series model of the fault system is established, and some kernel functions of functional series are obtained. Secondly, the coupling frequency relationship is established and the recursive search algorithm of frequency energy is applied to decouple the compound fault coupling frequency into a single fault frequency feature set. Finally, the threshold method of fault characteristic frequency energy entropy is utilized to optimize the single fault frequency feature set and identify the true and false features, so as to identify each characteristic frequency point of the composite fault. Experimental results show that, under the condition of low SNR, the proposed method can decouple no more than three typical composite fault signals without depending on the signal filter. [ABSTRACT FROM AUTHOR]

In order to enhance the classification accuracy and the generalization performance of the SVM classifier in cable partial discharge (PD) pattern recognition, a firefly optimized sparrow search algorithm (FoSSA) is proposed to optimize its kernel function parameters and penalty factors. First, the Circle-Gauss hybrid mapping model is employed in the population initialization stage of the sparrow search algorithm (SSA) to eliminate the uneven population distribution of random mapping. Sparrows tend to fall into local extremums during the search process, while the firefly algorithm has a fast optimization speed and strong local search ability. Thus, a firefly disturbance is added in the sparrow search process, and the fitness value is recalculated to update the sparrow position to enhance the sparrow's local optimization ability and accuracy. Finally, based on the SSA, a dynamic step-size strategy is adopted to make the step size dynamically decrease with the number of iterations and improve the accuracy of convergence. Six benchmark functions are employed to evaluate the optimization performance of the FoSSA quantitatively. Experiment results show that the recognition accuracy of the PD patterns using the SVM optimized by the FoSSA could reach 97.5%. [ABSTRACT FROM AUTHOR]

Due to the large fluctuation of import and export volume and many influencing factors, it is difficult for the general prediction algorithm to obtain more accurate prediction results. To solve this problem, a trade forecasting method based on the Particle Swarm Optimization (PSO) optimization hybrid Relevance Vector Machine (RVM) model is proposed. The method firstly finds out the indexes that affect the import and export trade and extracts the principal factors of the indexes as the input data of the model through principal component analysis. Then, based on the single-kernel RVM model training with multiple different kernel functions, the multikernel weighting method was used to construct the hybrid kernel RVM model according to the prediction error of the single-kernel RVM model. Finally, the parameters of the hybrid kernel model were optimized by PSO to improve the prediction accuracy. Close trade will strengthen the dependence between countries, and under this premise, it becomes particularly important to study the frequency of trade between countries. In this paper, the countries along the Belt and Road are classified by the method of high-order directed graph clustering, and the trade transactions between the countries are represented by a small network subgraph. Then, the 65 trading countries are classified by cutting graph and K-means clustering method, and the classification results are obtained by running relevant codes in MATLAB. The results are represented by the lattice graph. [ABSTRACT FROM AUTHOR]

Objective. Early diagnosis and treatment of occupational pneumoconiosis can delay the development of the disease. This study is aimed at investigating the intelligent diagnosis of occupational pneumoconiosis by wavelet transform-derived entropy. Method. From June 2013 to June 2020, the high KV digital radiographs (DR) and computed tomography (CT) images from a total of 60 patients with occupational pneumoconiosis in our department were selected. The wavelet transform-derived texture features were extracted from all images, and the decision tree was used for feature selection. The support vector machines (SVM) with three kernel functions were selected to classify the two kinds of images, and their diagnostic efficiency was compared. Result. After eight times of wavelet decomposition, eight wavelet entropy texture features (feature set) were extracted, and six were selected to form the feature subset. The classification effect of linear kernel function SVM is better than those of other functions, with an accuracy of 84.2%. The diagnostic values of DR and CT for occupational pneumoconiosis were the same (kappa = 0.737 , P < 0.001). The detection rate of CT for stage I of occupational pneumoconiosis was significantly higher than that of DR (P = 0.031). Conclusion. It is helpful to improve the early diagnosis level of pneumoconiosis by using SVM to make an intelligent diagnosis based on the wavelet entropy. [ABSTRACT FROM AUTHOR]

The aim of this research was to analyze the application of fuzzy C-means (FCM) algorithm-based ARM-Linux-embedded system in magnetic resonance imaging (MRI) images for prediction of brain tumors. The optimized FCM (OFCM) algorithm was proposed based on kernel function, and the ARM-Linux-embedded imaging system was designed under ARM9 chip and Linux recorder, which were applied in MRI images of brain tumor patients. It was found that the sensitivity, specificity, and accuracy of the OFCM algorithm (90.46%, 88.97%, and 97.46%) were greater obviously than those of the deterministic C-means clustering algorithm (80.38%, 77.98%, and 85.24%) and the traditional FCM algorithm (83.26%, 79.56%, and 86.45%), and the difference was statistically substantial (P < 0.05). The ME and running time of the OFCM algorithm decreased sharply in contrast to those of the deterministic C-means clustering algorithm and the traditional FCM algorithm (P < 0.05). There were great differences in fraction anisotropy (FA) and mean diffusion (MD) of tumor parenchymal area, surrounding edema area, and normal white matter area (P < 0.05). FA of stage III+IV was smaller than those of stage I and II (P < 0.05), while the apparent diffusion coefficient (ADC) of stage III+IV was greater than that of stage I and II (P < 0.05). In conclusion, the poor update data processing and low data clustering efficiency of FCM were solved by OFCM. Moreover, computational efficiency of ARM-Linux-embedded imaging system was improved, so as to better realize the prediction of brain tumor patients through ARM-Linux-embedded system based on adaptive FCM incremental clustering algorithm. [ABSTRACT FROM AUTHOR]

The main objective of this article is to establish generalized fractional Hermite–Hadamard and related type integral inequalities for h -Godunova–Levin convexity and h -Godunova–Levin preinvexity with extended Wright generalized Bessel function acting as kernel. Moreover, Hermite–Hadamard-type and trapezoid-type inequalities for several known convexities including Godunova–Levin function, classical convex, s -Godunova–Levin function, P -function, and s -convex function are deduced as corollaries. These obtained results are analyzed in the form of generalization of fractional inequalities. [ABSTRACT FROM AUTHOR]

In the present study, fractional variants of Hermite–Hadamard, Hermite–Hadamard–Fejér, and Pachpatte inequalities are studied by employing Mercer concept. Firstly, new Hermite–Hadamard–Mercer-type inequalities are presented for harmonically convex functions involving fractional integral operators with exponential kernel. Then, weighted Hadamard–Fejér–Mercer-type inequalities involving exponential function as kernel are proved. Finally, Pachpatte–Mercer-type inequalities for products of harmonically convex functions via fractional integral operators with exponential kernel are constructed. [ABSTRACT FROM AUTHOR]

This paper is aimed at presenting the unified integral operator in its generalized form utilizing the unified Mittag-Leffler function in its kernel. We prove the boundedness of this newly defined operator. A fractional integral operator comprising a unified Mittag-Leffler function is used to establish further Minkowski-type integral inequalities. Several related fractional integral inequalities that have recently been published in various articles can be inferred. [ABSTRACT FROM AUTHOR]

Online education is a popular way for college students at present, and it is also a good compensation way to meet the special situation that traditional offline teaching cannot complete the teaching task. Traditional classroom teaching methods have been difficult to meet the learning requirements of contemporary college students, while online classroom has made up for the shortcomings of traditional classroom teaching to some extent because of its short class hours, prominent focus, and online mobile learning. First, this paper proposes an online SSL (small sample learner) model for college students to integrate healthy emotional factors. The characteristics of learners are divided into three categories: basic characteristics of learners, characteristics of behavioral factors, and characteristics of emotional factors, and the problem of solving mapping functions is transformed into the problem of solving kernel functions. Second, a novel curriculum recommendation model integrating healthy emotional factors is proposed, which fully considers the influence of user comments on similarity and transforms the similarity of users in the overall score of the project into the similarity of users in the emotional tendency of the special attributes of the project. Through the experimental evaluation, the accuracy and stability of the recommendation are greatly improved. [ABSTRACT FROM AUTHOR]

Materials discovery is usually done using high-throughput computational screening. The use of costly and complex direct density functional theory (DFT) simulation methods has been commonly used to determine subtle trends in spin-state ordering and inorganic bonding of inorganic materials and, in general, to predict the electronic structure properties of transition metal complexes. A Gaussian process regression (GPR) framework consisting of four kernel functions is introduced for spin-state splitting estimation through inorganic chemistry-appropriate empirical inputs. To this end, the present study reviewed an extensive range of data values from earlier works. According to statistical analysis, the GPR model showed very good performance. The coefficients of determination were calculated to be 0.986 for the exponential and Matern kernel functions, suggesting the highest predictive power of these methods. Moreover, the sensitivity of output to inputs was measured. Artificial intelligence (AI) helped accurately predict the target values through various input ranges. [ABSTRACT FROM AUTHOR]

This paper focuses on the stabilization problem for the linear parabolic system using the backstepping method. The exponentially stability results for considered parabolic system are derived in two cases with Dirichlet and Neumann local terms. Also, the boundary conditions for the problem is assumed to be mixed or Robin-type boundary conditions. The main aim is to achieve the stability of the considered system using the backstepping method with help of Volterra integral transformation. The explicit solutions of kernel functions in integral transformation is obtained by using Laplace transform and designed a boundary control law to the closed-loop system. Finally, the effectiveness and applicability of the derived results are validated through a single-species pattern generation model. [ABSTRACT FROM AUTHOR]

The article titled "Positive Weighted Symmetry Function Kernels and Some Related Inequalities for a Generalized Class of Convex Functions" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

Heart diseases are a leading cause of death worldwide, and they have sparked a lot of interest in the scientific community. Because of the high number of impulsive deaths associated with it, early detection is critical. This study proposes a boosting Support Vector Machine (SVM) technique as the backbone of computer-aided diagnostic tools for more accurately forecasting heart disease risk levels. The datasets which contain 13 attributes such as gender, age, blood pressure, and chest pain are taken from the Cleveland clinic. In total, there were 303 records with 6 tuples having missing values. To clean the data, we deleted the 6 missing records through the listwise technique. The size of data, and the fact that it is a purely random subset, made this approach have no significant effect for the experiment because there were no biases. Salient features are selected using the boosting technique to speed up and improve accuracies. Using the train/test split approach, the data is then partitioned into training and testing. SVM is then used to train and test the data. The C parameter is set at 0.05 and the linear kernel function is used. Logistic regression, Nave Bayes, decision trees, Multilayer Perceptron, and random forest were used to compare the results. The proposed boosting SVM performed exceptionally well, making it a better tool than the existing techniques. [ABSTRACT FROM AUTHOR]

A synthetic aperture radar (SAR) target recognition method combining linear and nonlinear feature extraction and classifiers is proposed. The principal component analysis (PCA) and kernel PCA (KPCA) are used to extract feature vectors of the original SAR image, respectively, which are classical and reliable feature extraction algorithms. In addition, KPCA can effectively make up for the weak linear description ability of PCA. Afterwards, support vector machine (SVM) and kernel sparse representation-based classification (KSRC) are used to classify the KPCA and PCA feature vectors, respectively. Similar to the idea of feature extraction, KSRC mainly introduces kernel functions to improve the processing and classification capabilities of nonlinear data. Through the combination of linear and nonlinear features and classifiers, the internal data structure of SAR images and the correspondence between test and training samples can be better investigated. In the experiment, the performance of the proposed method is tested based on the MSTAR dataset. The results show the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

A synthetic aperture radar (SAR) target recognition method combining linear and nonlinear feature extraction and classifiers is proposed. The principal component analysis (PCA) and kernel PCA (KPCA) are used to extract feature vectors of the original SAR image, respectively, which are classical and reliable feature extraction algorithms. In addition, KPCA can effectively make up for the weak linear description ability of PCA. Afterwards, support vector machine (SVM) and kernel sparse representation-based classification (KSRC) are used to classify the KPCA and PCA feature vectors, respectively. Similar to the idea of feature extraction, KSRC mainly introduces kernel functions to improve the processing and classification capabilities of nonlinear data. Through the combination of linear and nonlinear features and classifiers, the internal data structure of SAR images and the correspondence between test and training samples can be better investigated. In the experiment, the performance of the proposed method is tested based on the MSTAR dataset. The results show the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the shortcomings of a single machine learning model with low model prediction accuracy and insufficient generalization ability in house price index prediction, a whale algorithm optimized support vector regression model based on bagging ensemble learning method is proposed. Firstly, gray correlation analysis is used to obtain the main influencing factors of house prices, and the segmentation forecasting method is used to divide the data set and forecast the house prices in the coming year using the data of the past ten years. Secondly, the whale optimization algorithm is used to find the optimal parameters of the penalty factor and kernel function in the SVR model, and then, the WOA-SVR model is established. Finally, in order to further improve the model generalization capability, a bagging integration strategy is used to further integrate and optimize the WOA-SVR model. The experiments are conducted to forecast the house price indices of four regions, Beijing, Shanghai, Tianjin, and Chongqing, respectively, and the results show that the prediction accuracy of the proposed integrated model is better than the comparison model in all cases. [ABSTRACT FROM AUTHOR]

The excavation damage of deep tunnels is one of the most important factors contributing to the failure of tunnel structures. In order to investigate the influence of tunnel shapes and fissure geometries, the kernel function in the traditional SPH method has been improved, which can realize the brittle fracture characteristics of particles and can be called the Improved Kernel of Smoothed Particle Hydrodynamics (IKSPH-2D). Meanwhile, the random fissure generation method in IKSPH has been put forward. Different tunnel shapes, fissure geometries, and locations are considered during the simulation of tunnel excavation, and results show that (1) the typical "V"-shaped shear damage zones appear after the tunnel excavation, which is consistent with engineering practice. Meanwhile, tunnel excavation also has an "activating" effect on the preexisting fissures. (2) The stability of circular-shaped tunnel is the best, while horseshoe shaped tunnel is worse, and the "U"-shaped tunnel is the worst. (3) Fissures with small and large dip angles have the greatest influence on the stability of tunnel excavation. With the increase of fissure numbers and lengths, the tunnel tends to be instable. (4) The IKSPH method gets free from traditional grids in FEM, which can dynamically reflect the fracture processes of tunnel excavation. Meanwhile, developing 3D IKSPH parallel program will be the future directions. [ABSTRACT FROM AUTHOR]

Many methods have been developed to derive respiration signals from electrocardiograms (ECGs). However, traditional methods have two main issues: (1) focusing on certain specific morphological characteristics and (2) not considering the nonlinear relationship between ECGs and respiration. In this paper, an improved ECG-derived respiration (EDR) based on empirical wavelet transform (EWT) and kernel principal component analysis (KPCA) is proposed. To tackle the first problem, EWT is introduced to decompose the ECG signal to extract the low-frequency part. To tackle the second issue, KPCA and preimaging are introduced to capture the nonlinear relationship between ECGs and respiration. The parameter selection of the radial basis function kernel in KPCA is also improved, ensuring accuracy and a reduction in computational cost. The correlation coefficient and amplitude square coherence coefficient are used as metrics to carry out quantitative and qualitative comparisons with three traditional EDR algorithms. The results show that the proposed method performs better than the traditional EDR algorithms in obtaining single-lead-EDR signals. [ABSTRACT FROM AUTHOR]

In recent years, deep learning methods which promote the accuracy and efficiency of fault diagnosis task without any extra requirement of artificial feature extraction have elicited the attention of researchers in the field of manufacturing industry as well as aerospace. However, the problems that data in source and target domains usually have different probability distributions because of different working conditions and there are insufficient labeled or even unlabeled data in target domain significantly deteriorate the performance and generalization of deep fault diagnosis models. To address these problems, we propose a novel Wasserstein Generative Adversarial Network with Gradient Penalty- (WGAN-GP-) based deep adversarial transfer learning (WDATL) model in this study, which exploits a domain critic to learn domain invariant feature representations by minimizing the Wasserstein distance between the source and target feature distributions through adversarial training. Moreover, an improved one-dimensional convolutional neural network- (CNN-) based feature extractor which utilizes exponential linear units (ELU) as activation functions and wide kernels is designed to automatically extract the latent features of raw time-series input data. Then, the fault model classifier trained in one working condition (source domain) with sufficient labeled samples could be generalized to diagnose data in other working conditions (target domain) with insufficient labeled samples. Experiments on two open datasets demonstrate that our proposed WDATL model outperforms most of the state-of-the-art approaches on transfer diagnosis tasks under diverse working circumstances. [ABSTRACT FROM AUTHOR]

Image recognition tasks involve an increasingly high amount of symmetric positive definite (SPD) matrices data. SPD manifolds exhibit nonlinear geometry, and Euclidean machine learning methods cannot be directly applied to SPD manifolds. The kernel trick of SPD manifolds is based on the concept of projecting data onto a reproducing kernel Hilbert space. Unfortunately, existing kernel methods do not consider the connection of SPD matrices and linear projections. Thus, a framework that uses the correlation between SPD matrices and projections to model the kernel map is proposed herein. To realize this, this paper formulates a Hilbert–Schmidt independence criterion (HSIC) regularization framework based on the kernel trick, where HSIC is usually used to express the interconnectedness of two datasets. The proposed framework allows us to extend the existing kernel methods to new HSIC regularization kernel methods. Additionally, this paper proposes an algorithm called HSIC regularized graph discriminant analysis (HRGDA) for SPD manifolds based on the HSIC regularization framework. The proposed HSIC regularization framework and HRGDA are highly accurate and valid based on experimental results on several classification tasks. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the time-fractional Zakharov-Kuznetsov equation (TFZKE) via natural transform decomposition method (NTDM) with nonsingular kernel derivatives. The fractional derivative considered in Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in Caputo sense (ABC). We employed natural transform (NT) on TFZKE followed by inverse natural transform, to obtain the solution of the equation. To validate the method, we have considered a few examples and compared with the actual results. Numerical results are in accordance with the existing results. [ABSTRACT FROM AUTHOR]