Kernel Type Research Articles

Vision-Based Defect Classification and Weight Estimation of Rice Kernels

Rice is one of the main staple food in many areas of the world. The quality estimation of rice kernels are crucial in terms of both food safety and socio-economic impact. This was usually carried out by quality inspectors in the past, which may result in both objective and subjective inaccuracies. In this paper, we present an automatic visual quality estimation system of rice kernels, to classify the sampled rice kernels according to their types of flaws, and evaluate their quality via the weight ratios of the perspective kernel types. To compensate for the imbalance of different kernel numbers and classify kernels with multiple flaws accurately, we propose a multi-stage workflow which is able to locate the kernels in the captured image and classify their properties. We define a novel metric to measure the relative weight of each kernel in the image from its area, such that the relative weight of each type of kernels with regard to the all samples can be computed and used as the basis for rice quality estimation. Various experiments are carried out to show that our system is able to output precise results in a contactless way and replace tedious and error-prone manual works.

Analysis of a chaotic system using fractal-fractional derivatives with exponential decay type kernels

<abstract><p>In this article, we introduce and analyze a novel fractal-fractional chaotic system. We extended the memristor-based chaotic system to the fractal-fractional mathematical model using Atangana-Baleanu–Caputo and Caputo-Fabrizio types of derivatives with exponential decay type kernels. We established the uniqueness and existence of the solution through Banach's fixed theory and Schauder's fixed point. We used some new numerical methods to derive the solution of the considered model and study the dynamical behavior using these operators. The numerical simulation results presented in both cases include the two and three-dimensional phase portraits and the time-domain responses of the state variables to evaluate the efficacy of both kernels.</p></abstract>

Semi-analytical and numerical computation of fractal-fractional sine-Gordon equation with non-singular kernels

<abstract><p>In this article, we study the nonlinear sine-Gordon equation (sGE) under Mittag-Leffler and exponential decay type kernels in a fractal fractional sense. The Laplace Adomian decomposition method (LADM) is applied to investigate the sGE under the above-mentioned operators. The convergence analysis is provided for the proposed method. The results are validated by considering numerical examples with different initial conditions for both kernels and confirm the competence of the proposed technique. It is revealed that the obtained series solutions of the model with fractal fractional operators converge to the exact solutions. The numerical results converge to the particular exact solutions, proving the significance of LADM for nonlinear systems under fractal fractional derivatives. The absolute error analysis between the exact and obtained series solutions with both operators is shown in the tabulated form. The physical interpretations of the attained results with different fractal and fractional parameters are discussed in detail.</p></abstract>

Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data.

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an -mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods

In this paper, we consider the Emden–Fowler integral equation with Green’s function type kernel. We propose three computational algorithms based on the Gegenbauer-wavelet, the Taylor-wavelet, and the Laguerre-wavelet to solve such problems. Firstly, we transform the given problems via the collocations technique to the system of algebraic equations, which are then solved by the Newton–Raphson method to get the required numerical solution. We also provide the error bound of the proposed method. To demonstrate the efficiency of the proposed methods, we consider several examples arising in physical models, including real-life problems. The numerical simulations justify the superiority and high performance of the methods, and the obtained results are compared with some other existing schemes. The comparison shows that the proposed method converges faster than other numerical techniques like Haar-wavelets collocation method, advanced Adomian decomposition method, and simplified reproducing kernel method. The numerical tables and graphs show that the accuracy of the proposed method is very high, even for the few collocation points. The L∞ and the L2 errors decrease gradually with an increase in collocation points, and hence, the current method is stable.

Predictive assessment of single-step BLUP with linear and non-linear similarity RKHS kernels: A case study in chickens.

Single-step GBLUP (ssGBLUP) to obtain genomic prediction was proposed in 2009. Many studies have investigated ssGBLUP in genomic selection in animals and plants using a standard linear kernel (similarity matrix) called genomic relationship matrix (G). More general kernels should allow capturing non-additive effects as well, whereas GBLUP is based on additive gene action. In this study, we generalized ssBLUP to accommodate two non-linear kernels, the averaged Gaussian kernel (AK) and the recently developed arc-cosine deep kernel (DK). We evaluated the methodology using body weight (BW) and hen-housing production (HHP) traits, recorded on a sample of phenotyped and genotyped commercial broiler chickens. There were, thus, different ssGBLUP models corresponding to G, AK and DK. We used random replication of training (TRN) and testing (TST) layouts at different genotyping rates (20%, 40%, 60% and 80% of all birds) in three selective genotyping scenarios. The selections were genotyping the youngest individuals in the pedigree (YS), random genotyping (RS) and genotyping based on parent average (PA). Predictive abilities were measured using rank correlations between the observed and the predictive phenotypic values in TST for each random partition. Prediction accuracy was influenced by the type of kernel when a large proportion of birds was genotyped. An advantage of non-linear kernels (AK and DK) was more apparent when 60 and 80% of birds had been genotyped. For BW, the lowest rank correlations were obtained with G (0.093±0.015 using RS by 20% genotyped individuals) and the highest values with DK (0.320±0.016 in the PA setting with 80% genotyped individuals). For HHP, the lowest and highest rank correlations were obtained by AK with 20% and 80% genotyped individuals, 0.071±0.016 (in RS) and 0.23±0.016 (in PA) respectively. Our results indicated that AK and DK are more effective than G when a large proportion of the target population is genotyped. Our expectation is that ssGBLUP with AK or DK models can perform even better than G when non-additive genetic effects influence the underlying variability of complex traits.

Differentiation between Epileptic and Psychogenic Nonepileptic Seizures in Electroencephalogram Using Wavelets and Support-Vector Machines

ABSTRACT The number of people suffering from epilepsy in the world exceeds 50 million and around 20% of this group refers to patients who have psychogenic nonepileptic seizures (PNES). Unlike epilepsy, PNES requires psychological treatment. When not correctly diagnosed, these patients can be submitted to a treatment based on antiepileptic drugs besides specific procedures for epilepsy. In this work, we propose the identification of patients with PNES from those with epilepsy using electroencephalogram (EEG) signals. Discrete Wavelet Transform (DWT) decomposition and a Support-Vector Machine (SVM) classifier were employed. Common types of wavelet families and SVM kernels were combined and compared. The results obtained for accuracy, sensitivity, and specificity are equal to 100% for the set of configuration parameters composed of windows encompassing whole seizures, wavelet Coiflet 1, and SVM kernel sigmoid or RBF. The proposed method is efficient and feasible to be applied to new patients admitted in a hospital center, even without having their previous EEG signals already collected. The main advantages of the proposed work are not requiring the use of accelerometer nor electromyographic signals, not being patient specific and outperforming other works results.

A predictor-corrector affine scaling method to train optimized extreme learning machine

Optimized extreme learning machine (OELM) has been shown to achieve high performance on classification problems due to its simple dual form. This paper presents a predictor-corrector affine scaling interior point method to exploit the dual problem of OELM. This method aims to combine a predictor step with a corrector step for determining the descent Newton direction. At each iteration, the predictor step focuses on the complementarity gap reduction and computes an affine scaling direction to estimate the extent of the reduction of complementarity gap, while the corrector step traces the central path towards the optimal solution by high order approximation, and computes the corresponding center direction. Then, the Newton direction is combined by using both two directions, and the iteration sequence of interior feasible points converges to the optimal solution. Extensive experimental evaluations on various benchmark datasets show that the proposed algorithms outperform other interior point-based or active set-based algorithms. Moreover, they are able to converge in fewer iterations, which are independent of kernel type, dataset size and dimensionality.

HEART DISEASE PREDICTION SYSTEM USING MACHINE LEARNING ALGORITHM

Abstract—Information decision support systems are becomingmore in use as we are living in the era of digital data andrise of artificial intelligence. Heart disease as one of the mostknown and dangerous is getting very important attention, thisattention is translated into digital and prediction system thatdetects the presence of disease according to the available dataand information. Such systems faced a lot of problems since thefirst rise, but now with the deveolopment of machine learnigfield we are using them in developing new models to detect thepresence of this disease, in addition to algorithms data is veryimportant which also form the heart of the predicton systems,as we know prediction algorithms take decisions and thesedecisions must be based on facts, and these facts are extractedfrom data, as a result data is the starting point of every system.In this paper we propose a Heart Disease Prediction Systemusing Machine Learning Algorithms, in terms of data we usedCleveland dataset, this dataset is normalized then divided intothree scnearios in terms of traning and testing respectively,80%-20%, 50%-50%, 30%-70%. In each case of dataset ifit is normalized or not we will have these three scenarios.We used three machine learning algorithms for every scenarioof the mentioned before which are SVM, SMO and MLP, inthese algorithms we’ve used two different kernels to test theresults upon that. These two types of simulation are added tothe collection of scenarios mentioned above to become as thefollowing we have at the main level two types normalized andunnormalized dataset, then for each one we have three typesaccording to the amount of training and testing dataset, thenfor each of these scenarios we have two scenarios according tothe type of kernel to become 30 scenarios in total, our proposedsystem have shown a dominance in terms of accuracy over theother previous works.

Identification of a Suitable Machine Learning Model for Detection of Asymptomatic Ganoderma boninense Infection in Oil Palm Seedlings Using Hyperspectral Data

In Malaysia, oil palm industry has made an enormous contribution to economic and social prosperity. However, it has been affected by basal stem rot (BSR) disease caused by Ganoderma boninense (G. boninense) fungus. The conventional practice to detect the disease is through manual inspection by a human expert every two weeks. This study aimed to identify the most suitable machine learning model to classify the inoculated (I) and uninoculated (U) oil palm seedlings with G. boninense before the symptoms’ appearance using hyperspectral imaging. A total of 1122 sample points were collected from frond 1 and frond 2 of 28 oil palm seedlings at the age of 10 months old, with 540 and 582 reflectance spectra extracted from U and I seedlings, respectively. The significant bands were identified based on the high separation between U and I seedlings, where the differences were observed significantly in the NIR spectrum. The reflectance values of each selected band were later used as input parameters of the 23 machine learning models developed using decision trees, discriminant analysis, logistic regression, naïve Bayes, support vector machine (SVM), k-nearest neighbor (kNN), and ensemble modelling with various types of kernels. The bands were optimized according to the classification accuracy achieved by the models. Based on the F-score and performance time, it was demonstrated that coarse Gaussian SVM with 9 bands performed better than the models with 35, 18, 14, and 11 bands. The coarse Gaussian SVM achieved an F-score of 95.21% with a performance time of 1.7124 s when run on a personal computer with an Intel® Core™ i7-8750H processor and 32 GB RAM. This early detection could lead to better management in the oil palm industry.

Outlier Detection On Graduation Data Of Darussalam Gontor University Using One-Class Support Vector Machine

Outlier detection is an important field of study because it is able to detect abnormal data distribution from a set of data. In the student graduation data, there are students with high semester GPA but do not graduate on time but students with low semester GPA can graduate on time. This study aims to detect outlier values ​​in student graduation data for the 2020-2021 class. Factors (attributes) used in this study are Student Academic Support Credit Scores (AKPAM) and Social Studies from semester one to semester six. The dataset used is 1204 graduates. The outlier detection method used is One-Class Support Vector Machine (SVM). One-class SVM is a derivative of SVM method that detects outliers based on data outside the specified class. The results of outlier detection using One-Class SVM method with three types of kernels produce the following reference values: kernel 'rbf' n by 91.4%, kernel 'linear' by 90% and kernel 'poly' by 90%. After normalization using MinMaxScaler the reference value increased by 2% in each kernel. The results of testing the One-Class SVM method get an average 90.3%, thus it can be concluded that the One-Class SVM method is feasible to be used as an outlier detection method.

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

Abstract The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

We study in which way a priori information on the independence of random variables affects the approximation accuracy of a nonparametric estimate of the Rosenblatt–Parzen probability density. A new technique for generating sets of independent components of a multidimensional random variable is proposed. The methodology is based on testing the hypotheses of the independence of combinations of the multidimensional random variable components using a two-alternative nonparametric kernel algorithm for pattern recognition corresponding to the maximum likelihood criterion. Classes correspond to the domains of definition of the probability densities of sets of independent and dependent components of the multidimensional random variable. Nonparametric statistics of the kernel type are used to estimate the probability densities. The choice of the bandwidths of the kernel estimates of the probability densities is made from the condition of the minimum root-mean-square criterion. The sequential procedure for generating a set of independent components begins with the analysis of paired combinations of components of a multidimensional random variable. For each pair of components, the probability of an error in recognizing classes corresponding to the assumptions of independence and dependence of the considered components is estimated. A pair of components with the maximum difference between these errors is determined. If the errors obtained do not differ significantly, then there are no independent components in the considered multivariate random variable. If there is a significant difference in the probability estimates of class recognition errors, a pair of independent components is established. These components are included in a three-component set of a multidimensional random variable. The analysis of their combinations is carried out in the same way, following the above-described procedure. The process of generating the set of independent components is stopped when no reliable difference occurs any more between the probabilities of errors in recognizing situations belonging to the accepted classes. In this case, the previous set of independent components is the desired result. In contrast to the traditional methodology based on the Pearson criterion, the proposed approach allows us to bypass a problem of the decomposition of the range of values of random variables into multidimensional intervals. The method of generating a set of independent components of a multidimensional random variable is illustrated by the results of the analysis of spectral features of remote sensing data of forest tracts using space imagery from the Landsat-8 satellite.

Tide Prediction in Prigi Beach using Support Vector Regression (SVR) Method

Purpose: Prigi Beach has the largest fishing port in East Java, but the topography of this beach is quite gentle, so it is prone to disasters such as tidal flooding. The tides of seawater strongly influence the occurrence of this natural event. Therefore, information on tidal level data is essential. This study aims to provide information about tidal predictions.Methods: In this case using the SVE method. Input data and time were examined using PACF autocorrelation plots to form input data patterns. The working principle of SVR is to find the best hyperplane in the form of a function that produces the slightest error.Result: The best SVR model built from the linear kernel, the MAPE value is 0.5510%, the epsilon is 0.0614, and the bias is 0.6015. The results of the tidal prediction on Prigi Beach in September 2020 showed that the highest tide occurred on September 19, 2020, at 10.00 PM, and the lowest tide occurred on September 3, 2020, at 04.00 AM. Value: After conducting experiments on three types of kernels on SVR, it is said that linear kernels can predict improvements better than polynomial and gaussian kernels.

Adaptive particle refinement strategies in smoothed particle hydrodynamics

Adaptive particle refinement (APR) can increase the efficiency of mesh-free particle methods by splitting mother particles into smaller daughter particles. However, most APR algorithms are based on solving a minimization problem in which a single mother particle is split into several daughter particles. This may cause insufficient accuracy because APR is typically adopted in problems where many mother particles are involved in splitting, and a superposition effect may occur in the refinement error field between neighboring mother particles. Hence, we develop a novel APR strategy for the smoothed particle hydrodynamics (SPH) method based on direct splitting multiple mother particles to obtain more accurate optimal APR parameters. In addition, angular momentum conservation conditions are derived and a new algorithm is proposed to implement periodic boundary conditions for open-channel flows. Furthermore, for the first time, we conduct a rigorous parametric study to investigate factors affecting the optimal APR parameters, including the split patterns, kernel types, the density calculation algorithms as well as refinement error definitions. This APR strategy is validated through five benchmark test cases. Test results show that the proposed algorithm can both improve the simulation accuracy, reduce the computational cost and show good flexibility for implementation.

Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel

Fractal-fractional operators have been crucial in detecting some hidden chaotic phenomena that could not be exposed using classical or simple fractional differential and integral operators. To provide new possibilities for capturing more chaotic behaviors, the present study is carried out for the dynamics of a new chaotic system by implementing fractal-fractional differential operator of Mittag-Leffler type kernel. It is also theoretically proved that the present model will have at least one solution and it will also have a unique solution. Numerical scheme is implemented through MATLAB software for the graphical solution of the proposed problem. Some results are found and portrayed through different graphs.

Calderón-Zygmund operators with kernels of Dini's type and their multilinear commutators on generalized variable exponent Morrey spaces

Calderón-Zygmund operators with kernels of Dini's type and their multilinear commutators on generalized variable exponent Morrey spaces

Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel type operator known as the Atangana-Baleanu-Caputo (ABC) derivative. We parametrize the model adopting available information of the disease from Pakistan in the period 9 April to 2 June 2020. We obtain the required solution with the help of a hybrid method, which is a combination of the decomposition method and the Laplace transform. Furthermore, a sensitivity analysis is carried out to evaluate the parameters that are more sensitive to the basic reproduction number of the model. Our results are compared with the real data of Pakistan and numerical plots are presented at various fractional orders.

APPROXIMATE SOLUTION OF FORNBERG–WHITHAM EQUATION BY MODIFIED HOMOTOPY PERTURBATION METHOD UNDER NON-SINGULAR FRACTIONAL DERIVATIVE

The basic idea of this paper is to investigate the approximate solution to a well-known Fornberg–Whitham equation of arbitrary order. We consider the stated problem under [Formula: see text] fractional order derivative. The proposed derivative is non-local and contains non-singular kernel of Mittag-Leffler type. With the help of Modified Homotopy Perturbation Method (MHPM), we find approximate solution to the aforesaid equations. The required solution is computed in the form of infinite series. The method needs no discretization or collocation and easy to implement to compute the approximate solution that we intend. We also compare our results with that of the exact solution for the initial four terms approximate solution as well as with that computed by the Laplace decomposition method. We also plot the approximate solution of considered model through surface plots. For numerical illustration, we use Matlab throughout this work.