Nonlinear Kernel Research Articles

Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing.

Edge mis-figures are regarded as one of the most difficult technical issues in optical fabrication. At present, only the near straight-line edge tool influence function (TIF) can be fitted by a polynomial function, but it is difficult to unify a 2-D analytical model suitable for complex edge workpieces and various tools, due to the lack of the scientific understanding of the edge removal behavior. In this paper, a comprehensive mathematical model is proposed to reveal the mechanism of the edge effect and accurately predict the complex edge TIF. The concept of a nonlinear edge kernel is first proposed and verified that the nonlinear pressure can be characterized by convoluting the kernel with the edge contour, which can be easily adapted to complex edge cases; besides, the edge kernel obtaining algorithm is established. The linear pressure part is verified to be constrained by the moment balance formula, which occurs in universal joint tool. Besides, the basic pressure distribution is presented to compensate the pressure distortion caused by the uneven form of the tool pad. The introducing of these three parts makes the complex edge pressure modeled efficiently and matched perfectly with the FEA results. In addition, a series of TIF experiments were carried out on various complex edge workpieces and different tools, which could be well predicted by the proposed model in 2-D view.

The use of measurable traits of trunk and crown to assess the biosocial classes of oak trees (Quercus robur L.)

The crown class assessment is a key element in forestry practice. It is a traditional method that finds application in thinning plans, assessment of site index, tree competition, or crown condition. Assigning trees into a given class is done during field surveys and requires precision and experience to avoid inaccuracy. Therefore, Kraft’s system has often been criticized and modified. Thus, in our study, we aimed to analyse whether the directly measured traits of trunk and crown of oak trees (Quercus robur L.) can be applied to crown class assessment. For this purpose, we used the principal component analysis (PCA) and nonlinear kernel principal component analysis (KPCA) based on measurable traits of trunk and crown, i.e., the height of the tree, the diameter at breast height, the length of the crown, and the field crown projection area. In total, we measured 286 mature trees in three oak stands located in western Poland. Results indicate that all chosen traits of trunk and crown allowed, though not always perfect, to assign the trees into given crown classes. The greatest contribution to crown class distinction had the diameter at breast height and the parameters of crown, i.e., and the field crown projection area. Furthermore, results show that the best method of assigning the trees into biosocial classes is the KPCA Gauss, considering the percentage explanation of the total variability, and KPCA Laplace, considering the visual division. In the latter, the multivariate analysis resulted in a similar crown class assignment as the field-assigned method. However, its application requires measurements that make it neither cheaper nor faster than a traditional crown class assessment. It indicates that a traditional field-assigned method, despite its subjectivity, should continue to be of great importance in forestry practice. Moreover, the alternative traits of trunk and crown can be a potentially useful statistical substitute for crown class assessment. Keywords: crown class, oak stand, trunk and crown traits, multivariate methods

Nonlocal effects in a functionally graded thermoelastic layer due to volumetric absorption laser

The primary focus of the present contribution is to develop a new system of differential equations describing the nonlocal thermoelasticity theory. The problem deals with the thermoelastic interaction in a nonhomogeneous thermoelastic layer induced by absorbing penetrating laser radiation throughout its volume. The heat conduction equation has been formulated in the context of memory dependent three-phase lag model. The surfaces of the layer are thermally insulated and free of traction. Employing the integral Laplace transform technique, the solutions of the field quantities have been achieved in the transformed domain. The corresponding solutions in the space–time domain have been derived using the numerical inversion of the Laplace transform by Riemann-sum approximation technique. The numerical estimates of the field quantities have been depicted graphically to address the effects of nonlocality and memory effects on the temperature profile, displacement and stress components. The effect of the delay time, nonhomogeneity and various choices of linear and nonlinear kernel functions in the heat transport law have also been reported.

Minimizing makespan under data prefetching constraints for embedded vision systems: a study of optimization methods and their performance

In confronting the “Memory Wall”, the design of embedded vision systems exhibits many challenges regarding design cost, energy consumption, and performance. This paper considers a variant of the Job Shop Scheduling Problem with tooling constraints, arising in this context, in which the completion time (makespan) is to be minimized. This objective corresponds to the performance of the produced circuit. We discuss different formulations using integer linear programming and point out their characteristics, namely the size and the quality of the linear programming relaxation bound. To solve this scheduling problem with large size, we compare various approaches, including a Constraint Programming model, two constructive greedy heuristics, two models of LocalSolver, a Simulated Annealing algorithm, and a Beam Search algorithm. Numerical experiments are conducted on 16 benchmark instances from the literature and 12 real-life non-linear image processing kernels for validating their efficiency.

Genomic Prediction of Grain Yield in a Barley MAGIC Population Modeling Genotype per Environment Interaction.

Multi-parent Advanced Generation Inter-crosses (MAGIC) lines have mosaic genomes that are generated shuffling the genetic material of the founder parents following pre-defined crossing schemes. In cereal crops, these experimental populations have been extensively used to investigate the genetic bases of several traits and dissect the genetic bases of epistasis. In plants, genomic prediction models are usually fitted using either diverse panels of mostly unrelated accessions or individuals of biparental families and several empirical analyses have been conducted to evaluate the predictive ability of models fitted to these populations using different traits. In this paper, we constructed, genotyped and evaluated a barley MAGIC population of 352 individuals developed with a diverse set of eight founder parents showing contrasting phenotypes for grain yield. We combined phenotypic and genotypic information of this MAGIC population to fit several genomic prediction models which were cross-validated to conduct empirical analyses aimed at examining the predictive ability of these models varying the sizes of training populations. Moreover, several methods to optimize the composition of the training population were also applied to this MAGIC population and cross-validated to estimate the resulting predictive ability. Finally, extensive phenotypic data generated in field trials organized across an ample range of water regimes and climatic conditions in the Mediterranean were used to fit and cross-validate multi-environment genomic prediction models including G×E interaction, using both genomic best linear unbiased prediction and reproducing kernel Hilbert space along with a non-linear Gaussian Kernel. Overall, our empirical analyses showed that genomic prediction models trained with a limited number of MAGIC lines can be used to predict grain yield with values of predictive ability that vary from 0.25 to 0.60 and that beyond QTL mapping and analysis of epistatic effects, MAGIC population might be used to successfully fit genomic prediction models. We concluded that for grain yield, the single-environment genomic prediction models examined in this study are equivalent in terms of predictive ability while, in general, multi-environment models that explicitly split marker effects in main and environmental-specific effects outperform simpler multi-environment models.

Deep Multiple Kernel Learning for Prediction of MicroRNA Precursors

MicroRNAs are a group of noncoding RNAs that are about 20–24 nucleotides in length. They are involved in the physiological processes of many diseases and regulate transcriptional and post-transcriptional gene expression. Therefore, the prediction of microRNAs is of great significance for basic biological research and disease treatment. MicroRNA precursors are the necessary stage of microRNA formation. RBF kernel support vector machines (RBF-SVMs) and shallow multiple kernel support vector machines (MK-SVMs) are often used in microRNA precursors prediction. However, the RBF-SVMs could not represent the richer sample features, and the MK-SVMs just use a simply convex combination of few base kernels. This paper proposed a localized multiple kernel learning model with a nonlinear synthetic kernel (LMKL-D). The nonlinear synthetic kernel was trained by a three-layer deep multiple kernel learning model. The LMKL-D model was tested on 2241 pre-microRNAs and 8494 pseudo hairpin sequences. The experiments showed that the LMKL-D model achieved 93.06% sensitivity, 99.27% specificity, and 98.03% accuracy on the test set. The results showed that the LMKL-D model can increase the complexity of kernels and better predict microRNA precursors. Our LMKL-D model can better predict microRNA precursors compared with the existing methods in specificity and accuracy. The LMKL-D model provides a reference for further validation of potential microRNA precursors.

WGNCS: A robust hybrid cross-version defect model via multi-objective optimization and deep enhanced feature representation

For a constantly-evolving software project with multiple releasing versions, Cross-Version Defect Prediction (CVDP) can identify the potential defect in the latter one by mining historical defect information from the prior releasing software versions. Unfortunately, the imbalanced class distribution and the complex intrinsic structure in software projects make it challenging to obtain suitable defect features and construct a predominant CVDP model. To address these challenges, we propose a robust hybrid CVDP model named WGNCS based on WGAN-GP (Wasserstein GAN with Gradient Penalty), multi-objective NSGA-III (Non-dominated Sorting Genetic Algorithm - III) algorithm and hybrid CNN-SVM (Convolutional Neural Network – Support Vector Machine) in this study, which has three main merits: (1) employ a powerful deep learning generative model – WGAN-GP to conduct data augmentation tasks, thereby achieving defect class balance and generating more training instances. (2) utilize the multi-objective NSGA-III algorithm to select the fewest representative training feature subset for the minimum error. (3) construct a single powerful defect predictor CNN-SVM by cascading a high-level deep semantic feature extractor (CNN) and a classifier (SVM) with the fixed non-linear Gaussian kernel function. We verify the CVDP performance of WGNCS on 32 cross-version pairs derived from 45 software project versions. The experimental results demonstrate that the WGNCS model can exhibit encouraging performance.

A novel multi-model data-driven ensemble approach for the prediction of particulate matter concentration.

Accuracy in the prediction of the particulate matter (PM2.5 and PM10) concentration in the atmosphere is essential for both its monitoring and control. In this study, a novel neuro fuzzy ensemble (NF-E) model was proposed for prediction of hourly PM2.5 and PM10 concentration. The NF-E involves careful selection of relevant input parameters for base modelling and using an adaptive neuro fuzzy inference system (ANFIS) model as a nonlinear kernel for obtaining ensemble output. The four base models used include ANFIS, artificial neural network (ANN), support vector regression (SVR) and multilinear regression (MLR). The dominant input parameters for developing the base models were selected using two nonlinear approaches (mutual information and single-input single-output ANN-based sensitivity analysis) and a conventional Pearson correlation coefficient. The NF-E model was found to predict both PM2.5 and PM10 with higher generalization ability and least error. The NF-E model outperformed all the single base models and other linear ensemble techniques with a Nash-Sutcliffe efficiency (NSE) of 0.9594 and 0.9865, mean absolute error (MAE) of 1.63 μg/m3 and 1.66 μg/m3 and BIAS of 0.0760 and 0.0340 in the testing stage for PM2.5 and PM10, respectively. The NF-E could improve the efficiency of other models by 4-22% for PM2.5 and 3-20% for PM10 depending on the model.

Small Flying Object Classifications Based on Trajectories and Support Vector Machines

This paper presents an alternative approach to identify and classify the group of small flying objects especially drones from others, notably birds and kites (inclusive of kiteflying), in near field, by examining the pattern of their flight paths and trajectories. The trajectories of the drones and other flying objects were extracted from multiple clips of videos including various natural and synthetic database. Four trajectories characteristics are observed and extracted from the object’s flight paths, i.e., heading or turning angle, curvature, pace velocity, and pace acceleration. Subsequently, principal component analyses were applied to reduce the number of these trajectory features from 4 to 2 parameters. Multi-class classification by support vector machine (SVM) with non-linear transformation kernel was used. Multiple classification models were developed by several algorithms with various transformation kernels. The hyperparameters were optimized using Bayesian optimization. The performances of the different models are compared through the prediction accuracy of the test data.

The role of feature space in atomistic learning

Efficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as the fact that each choice of features can lead to very different behavior depending on how they are used, e.g. by introducing non-linear kernels and non-Euclidean metrics to manipulate them, makes it difficult to objectively compare different methods, and to address fundamental questions on how one feature space is related to another. In this work we introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels, in terms of the structure of the feature space that they induce. We define diagnostic tools to determine whether alternative feature spaces contain equivalent amounts of information, and whether the common information is substantially distorted when going from one feature space to another. We compare, in particular, representations that are built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features. We also investigate the impact of different choices of basis functions and hyperparameters of the widely used SOAP and Behler–Parrinello features, and investigate how the use of non-linear kernels, and of a Wasserstein-type metric, change the structure of the feature space in comparison to a simpler linear feature space.

Genetic robust kernel sample selection for chemometric data analysis

AbstractIn this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi‐objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M‐regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

The Additive Input-Doubling Method Based on the SVR with Nonlinear Kernels: Small Data Approach

The problem of effective intellectual analysis in the case of handling short datasets is topical in various application areas. Such problems arise in medicine, economics, materials science, science, etc. This paper deals with a new additive input-doubling method designed by the authors for processing short and very short datasets. The main steps of the method should include the procedure of data augmentation within the existing dataset both in rows and columns (without training), the use of nonlinear SVR to implement the training procedure, and the formation of the result based on the author’s procedure. The authors show that the developed data augmentation procedure corresponds to the principles of axial symmetry. The training and application procedures of the method developed are described in detail, and two algorithmic implementations are presented. The optimal parameters of the method operation were selected experimentally. The efficiency of its work during the processing of short datasets for solving the prediction task was established experimentally by comparison with other methods of this class. The highest prediction accuracy based on both proposed algorithmic implementations of a method among all of the investigated ones was defined. The main areas of application of the developed method are described, and its shortcomings and prospects of further research are given.

Suspended sediment load prediction in consecutive stations of river based on ensemble pre-post-processing kernel based approaches

Abstract Sediment transportation and accurate estimation of its rate is a significant issue for river engineers and researchers. In this study, the capability of kernel based approaches including Kernel Extreme Learning Machine (KELM) and Gaussian Process Regression (GPR) was assessed for predicting the river daily Suspended Sediment Discharge (SSD). For this aim, the Mississippi River, with three consecutive hydrometric stations, was selected as the case study. Based on the sediment and flow characteristics during the period of 2005–2008, several models were developed and tested under two scenarios (i.e. modeling based on each station's own data or the previous stations' data). Two post-processing techniques, namely Wavelet Transform (WT) and Ensemble Empirical Mode Decomposition (EEMD), were used for enhancing the SSD modeling capability. Also, data post-proceeding was done using Simple Linear Averaging (SLAM) and Nonlinear Kernel Extreme Learning Machine Ensemble (NKELME) methods. Obtained results indicated that the integrated models resulted in more accurate outcomes. Data processing enhanced the models' capability up to 35%. It was found that SSD modeling based on the station's own data led to better results; however, using the integrated approaches, the previous station's data could be applied successfully for the SSD modeling when a station's own data were not available.

An asymptotic expansion for the fractional p-Laplacian and for gradient-dependent nonlocal operators

Mean value formulas are of great importance in the theory of partial differential equations: many very useful results are drawn, for instance, from the well-known equivalence between harmonic functions and mean value properties. In the nonlocal setting of fractional harmonic functions, such an equivalence still holds, and many applications are nowadays available. The nonlinear case, corresponding to the [Formula: see text]-Laplace operator, has also been recently investigated, whereas the validity of a nonlocal, nonlinear, counterpart remains an open problem. In this paper, we propose a formula for the nonlocal, nonlinear mean value kernel, by means of which we obtain an asymptotic representation formula for harmonic functions in the viscosity sense, with respect to the fractional (variational) [Formula: see text]-Laplacian (for [Formula: see text]) and to other gradient-dependent nonlocal operators.

Learning Kernel for Conditional Moment-Matching Discrepancy-Based Image Classification.

Conditional maximum mean discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions; thus, it has been successfully used for pattern classification. However, CMMD does not work well on complex distributions, especially when the kernel function fails to correctly characterize the difference between intraclass similarity and interclass similarity. In this paper, a new kernel learning method is proposed to improve the discrimination performance of CMMD. It can be operated with deep network features iteratively and thus denoted as KLN for abbreviation. The CMMD loss and an autoencoder (AE) are used to learn an injective function. By considering the compound kernel, that is, the injective function with a characteristic kernel, the effectiveness of CMMD for data category description is enhanced. KLN can simultaneously learn a more expressive kernel and label prediction distribution; thus, it can be used to improve the classification performance in both supervised and semisupervised learning scenarios. In particular, the kernel-based similarities are iteratively learned on the deep network features, and the algorithm can be implemented in an end-to-end manner. Extensive experiments are conducted on four benchmark datasets, including MNIST, SVHN, CIFAR-10, and CIFAR-100. The results indicate that KLN achieves the state-of-the-art classification performance.

Multifuse multilayer multikernel RVFLN+ of process modes decomposition and approximate entropy data from iEEG/sEEG signals for epileptic seizure recognition

In this paper, the extracted features using variational mode decomposition (VMD) and approximate entropy (ApEn) privileged information of the input EEG signals are combined with multilayer multikernel random vector functional link network plus (MMRVFLN+) classifier to recognize the epileptic seizure epochs efficaciously. In our experiment Bonn University single-channel intracranial electroencephalogram (iEEG) and Children's Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) multichannel scalp EEG (sEEG) recordings are considered to evaluate the efficacy of the proposed method. The VMD is applied on chaotic, non-stationary, nonlinear, and complex EEG signal to decompose it into three band-limited intrinsic mode functions (BLIMFs). The Hilbert transform (HT) is applied on BLIMFs to extract informative spectral and temporal features. The ApEn is computed from the raw EEG signals as the privileged information and given to the multi-hidden layer structure to obtain the most discriminative compressed form. The scatter plots show the distinct nature of compressed privileged ApEn information among the seizure pattern classes. The linear as well as nonlinear mapping, local and global kernel function, high-learning speed, less computationally complex MMRVFLN+ classifier is proposed to recognize the seizure events accurately by importing the efficacious features with ApEn as the input. The advanced signal processing algorithm i.e., Hilbert Huang transform (HHT) with ApEn and MMRVFLN+ are combined to compare the performance with the proposed VMDHTApEn-MMRVFLN+ method. The proposed method has remarkable recognition ability, superior classification accuracy, and excellent overall performance as compared to other methods. The digital architecture of the multifuse MMRVFLN+ is developed and implemented on a high-speed reconfigurable FPGA hardware platform to validate the effectiveness of the proposed method. The superior classification accuracy, the negligible false positive rate per hour (FPR/h), simplicity, feasibility, robustness, and practicability of the proposed method validate its ability to recognize the epileptic seizure epochs automatically.

Consistency and diversity neural network multi-view multi-label learning

In multi-view multi-label learning, each object is represented by multiple heterogeneous data and is simultaneously associated with multiple class labels. Previous studies usually use shared subspaces to fuse multi-view representations. However, as the number of views increases, it is more challenging to capture the high-order relationships among multiple views. Therefore, a novel neural network multi-view multi-label learning framework is proposed, which is intended to solve the problem of consistency and diversity among views through a simple and effective method(CDMM). First, we build a separate classifier for each view based on the neural network method of the nonlinear kernel mapping function and require each view to learn a consistent label result. Then, we consider the diversity of individual views while learning a consistent representation among views. For this reason, we combine the Hilbert–Schmidt Independence Criterion with exploring the diversity among different views. Finally, the label correlation factor is in addition to the classification model, and the view contribution factor is added to the prediction model. A large number of comparative experiments with existing state-of-the-art solutions on benchmark multi-view multi-label learning data sets show the effectiveness of this method.

Flaw characterization in conductive media based on pulsed Eddy current measurements: A fast non‐iterative inversion approach

This paper proposes a non-iterative procedure for flaw(s) characterization based on Pulsed Eddy Current Testing (PECT) signals analysis. The adopted inversion strategy is based on the use of supervised statistical learning algorithms. A numerical forward solver, based on the Finite Integration Technique (FIT), is used for the generation of the training data (the input-targets couples of the learning algorithm). Predictions are then carried out in almost real-time using a non-linear kernel based regression method, known as kernel ridge regression. It turns out that the direct fit of the regression model to the raw PECT signals may lead to poor prediction accuracy due to the large cardinality of PECT signals. To remedy this problem, an adaptive sampling strategy has been adopted in this work. The performance of the proposed methodology is discussed and compared with solutions proposed in the literature.

L1-norm Laplacian support vector machine for data reduction in semi-supervised learning

As a semi-supervised learning method, Laplacian support vector machine (LapSVM) is popular. Unfortunately, the model generated by LapSVM has a poor sparsity. A sparse decision model has always been fascinating because it could implement data reduction and improve performance. To generate a sparse model of LapSVM, we propose an $$\ell _1$$ -norm Laplacian support vector machine ( $$\ell _1$$ -norm LapSVM), which replaces the $$\ell _2$$ -norm with the $$\ell _1$$ -norm in LapSVM. The $$\ell _1$$ -norm LapSVM has two techniques that can induce sparsity: the $$\ell _1$$ -norm regularization and the hinge loss function. We discuss two situations for the $$\ell _1$$ -norm LapSVM, linear and nonlinear ones. In the linear $$\ell _1$$ -norm LapSVM, the sparse decision model implies that features with nonzero coefficients are contributive. In other words, the linear $$\ell _1$$ -norm LapSVM can perform feature selection to achieve the goal of data reduction. Moreover, the nonlinear (kernel) $$\ell _1$$ -norm LapSVM can also implement data reduction in terms of sample selection. In addition, the optimization problem of the $$\ell _1$$ -norm LapSVM is a convex quadratic programming one. That is, the $$\ell _1$$ -norm LapSVM has a unique and global solution. Experimental results on semi-supervised classification tasks have shown a comparable performance of our $$\ell _1$$ -norm LapSVM.

Epileptic Electroencephalogram Classification using Relative Wavelet Sub-Band Energy and Wavelet Entropy

Epilepsy is one of the common neurological disorders which can cause unprovoked seizures. Currently, diagnosis and evaluation are carried out using electroencephalogram (EEG) signal analysis, which is performed visually by clinicians. Since EEG signals tend to be random and non-stationary, the visual inspection often provides misrepresentation of results. Numerous studies have been proposed computer-based analysis for epileptic EEG classification; however, there is still a gap to improve detection accuracy with a small number of features. Therefore, in this study, we proposed an automatic detection protocol for epileptic EEG classification. The proposed methods are relative wavelet energy and wavelet entropy for feature extraction and combined with the classifier method for automatic detection. In this study, three classes of EEG consisted of pre-ictal, ictal, and interictal were used as test data and also evaluate the proposed method. EEG signals were decomposed using wavelet transform into five conventional sub-bands, including gamma, beta, alpha, theta, and delta. The relative energy and entropy were then calculated in each of these bands as a feature set. These methods are chosen with consider of low-cost computing. We tested the performance of our feature extraction method using Support Vector Machine (SVM), both linear and non-linear kernels. From the simulation, the highest accuracy was 80-96.7% for ictal vs. pre-ictal, ictal vs. inter-ictal, pre-ictal vs. inter-ictal, and ictal vs. non-ictal. Finally, this work was expected to help clinicians in the detection of epilepsy onset based on EEG signals.