Nonlinear Kernel Research Articles

RETRACTED ARTICLE: An efficient medical data classification using oppositional fruit fly optimization and modified kernel ridge regression algorithm

Medical researches utilize data mining techniques for several years and have been well known to be successful one. In the medical data have certain characteristic that make their analysis very challenging and attractive. In the proposed medical data classification research, it contains relevant and irrelevant features. Here the irrelevant features to be reduced with the aid of oppositional fruit fly optimization algorithm. In the feature selection phase the optimal subset of features are finally divided into training and testing files. The output of training and testing files is given into classifier. This classification is to be performed with the aid of Modified Kernel Ridge Regression (MKRR). KRR gets knowledge about a linear function in the space induced by the respective kernel and the data. For MKRR non-linear kernels, this corresponds to a non-linear function in the original space. The form of the model acquire knowledge by Kernel Ridge is alike to support vector regression.

A COMPREHENSIVE COMPARISON OF MACHINE LEARNING ALGORITHMS ON DIAGNOSING ASTHMA DISEASE AND COPD

Ponte Academic JournalMar 2020, Volume 76, Issue 3 A COMPREHENSIVE COMPARISON OF MACHINE LEARNING ALGORITHMS ON DIAGNOSING ASTHMA DISEASE AND COPDAuthor(s): Erkut Bolat ,Hasan Yildirim, Sedat Altin, Eray YurtsevenJ. Ponte - Mar 2020 - Volume 76 - Issue 3 doi: 10.21506/j.ponte.2020.3.17 Abstract:The diagnosis and classification of asthma and COPD, which are the most common respiratory diseases, have been vital importance. Recently, machine learning has been great interest for processing health data due to this importance. The focus of previous studies has been to obtain the most predictive algorithm for diagnosing aforementioned diseases. However, variable importance has received little attention. The principal objective of this study is to investigate machine learning algorithms both predictivity and variable importance evaluation abilities. A comprehensive comparison has been carried out by considering different performance criteria including accuracy, precision, recall, Kappa statistics, F-measure, ROC curve and AUC value. The findings have been indicated that Random forest (with CART learner), C5.0 for asthma and SVM (with non-linear kernel) and GBM for COPD are the best algorithms. While the most important variable for asthma is FEV3, MEF50 for COPD. FEV1 and FVC have been common variables among the top five variables. The rank of variables has been supported by statistical significance tests. Additionally, ROC curves and AUC values have provided similar and supportive results as visually. Consequently, this study should be of value to practitioners and researchers studying on expert systems on health sciences and machine learning applications. Download full text:Check if you have access through your login credentials or your institution Username Password

Application of Machine Learning to Predict Grain Boundary Embrittlement in Metals by Combining Bonding-Breaking and Atomic Size Effects.

The strengthening energy or embrittling potency of an alloying element is a fundamental energetics of the grain boundary (GB) embrittlement that control the mechanical properties of metallic materials. A data-driven machine learning approach has recently been used to develop prediction models to uncover the physical mechanisms and design novel materials with enhanced properties. In this work, to accurately predict and uncover the key features in determining the strengthening energies, three machine learning methods were used to model and predict strengthening energies of solutes in different metallic GBs. In addition, 142 strengthening energies from previous density functional theory calculations served as our dataset to train three machine learning models: support vector machine (SVM) with linear kernel, SVM with radial basis function (RBF) kernel, and artificial neural network (ANN). Considering both the bond-breaking effect and atomic size effect, the nonlinear kernel based SVR model was found to perform the best with a correlation of r2 ~ 0.889. The size effect feature shows a significant improvement to prediction performance with respect to using bond-breaking effect only. Moreover, the mean impact value analysis was conducted to quantitatively explore the relative significance of each input feature for improving the effective prediction.

Nonlinear Adaptive Filtering With Kernel Set-Membership Approach

This paper develops nonlinear kernel adaptive filtering algorithms based on the set-membership filtering (SMF) framework. The set-membership-based filtering approach is distinct from the conventional adaptive filtering approaches in that it aims for the filtering error being bounded in magnitude, as opposed to seeking to minimize the time average or ensemble average of the squared errors. The proposed kernel SMF algorithms feature selective updates of their parameter estimates by making discerning use of the input data, and selective increase of the dimension in the kernel expansion. These result in less computational cost and faster tracking without compromising the mean-squared error performance. We show, through convergence analysis, that the sequences of parameter estimates of our proposed algorithms are convergent, and the filtering error is asymptotically upper bounded in magnitude. Simulations are performed which show clearly the advantages of the proposed algorithms in terms of lower computational complexity, reduced dictionary size, and steady-state mean-squared errors comparable to existing algorithms.

Reliable Multi-kernel Subtask Graph Correlation Tracker.

Many astonishing correlation filter trackers pay limited concentration on the tracking reliability and locating accuracy. To solve the issues, we propose a reliable and accurate cross correlation particle filter tracker via graph regularized multi-kernel multi-subtask learning. Specifically, multiple non-linear kernels are assigned to multi-channel features with reliable feature selection. Each kernel space corresponds to one type of reliable and discriminative features. Then, we define the trace of each target subregion with one feature as a single view, and their multi-view cooperations and interdependencies are exploited to jointly learn multi-kernel subtask cross correlation particle filters, and make them complement and boost each other. The learned filters consist of two complementary parts: weighted combination of base kernels and reliable integration of base filters. The former is associated to feature reliability with importance map, and the weighted information reflects different tracking contribution to accurate location. The second part is to find the reliable target subtasks via the response map, to exclude the distractive subtasks or backgrounds. Besides, the proposed tracker constructs the Laplacian graph regularization via cross similarity of different subtasks, which not only exploits the intrinsic structure among subtasks, and preserves their spatial layout structure, but also maintains the temporal-spatial consistency of subtasks. Comprehensive experiments on five datasets demonstrate its remarkable and competitive performance against state-of-the-art methods.

Bayesian Uncertainty Quantification with Multi-Fidelity Data and Gaussian Processes for Impedance Cardiography of Aortic Dissection.

In 2000, Kennedy and O’Hagan proposed a model for uncertainty quantification that combines data of several levels of sophistication, fidelity, quality, or accuracy, e.g., a coarse and a fine mesh in finite-element simulations. They assumed each level to be describable by a Gaussian process, and used low-fidelity simulations to improve inference on costly high-fidelity simulations. Departing from there, we move away from the common non-Bayesian practice of optimization and marginalize the parameters instead. Thus, we avoid the awkward logical dilemma of having to choose parameters and of neglecting that choice’s uncertainty. We propagate the parameter uncertainties by averaging the predictions and the prediction uncertainties over all the possible parameters. This is done analytically for all but the nonlinear or inseparable kernel function parameters. What is left is a low-dimensional and feasible numerical integral depending on the choice of kernels, thus allowing for a fully Bayesian treatment. By quantifying the uncertainties of the parameters themselves too, we show that “learning” or optimising those parameters has little meaning when data is little and, thus, justify all our mathematical efforts. The recent hype about machine learning has long spilled over to computational engineering but fails to acknowledge that machine learning is a big data problem and that, in computational engineering, we usually face a little data problem. We devise the fully Bayesian uncertainty quantification method in a notation following the tradition of E.T. Jaynes and find that generalization to an arbitrary number of levels of fidelity and parallelisation becomes rather easy. We scrutinize the method with mock data and demonstrate its advantages in its natural application where high-fidelity data is little but low-fidelity data is not. We then apply the method to quantify the uncertainties in finite element simulations of impedance cardiography of aortic dissection. Aortic dissection is a cardiovascular disease that frequently requires immediate surgical treatment and, thus, a fast diagnosis before. While traditional medical imaging techniques such as computed tomography, magnetic resonance tomography, or echocardiography certainly do the job, Impedance cardiography too is a clinical standard tool and promises to allow earlier diagnoses as well as to detect patients that otherwise go under the radar for too long.

An efficient approach for physical actions classification using surface EMG signals.

Physical actions classification of surface electromyography (sEMG) signal is required in applications like prosthesis, and robotic control etc. In this paper, tunable-Q factor wavelet transform (TQWT) based algorithm is proposed for the classification of physical actions such as clapping, hugging, bowing, handshaking, standing, running, jumping, waving, seating, and walking. sEMG signal is decomposed into sub-bands by TQWT. Various features are extracted from each different band and statistical analysis is performed. These features are fed into multi-class least squares support vector machine classifier using two non-linear kernel functions, morlet wavelet function, and radial basis function. The proposed method is an attempt for classifying physical actions using TQWT and its performance and results are promising and have high classification accuracy of 97.74% for sub-band eight with morlet kernel function.

Thermoelastic response of fiber-reinforced epoxy composite under continuous line heat source

This present study deals with a novel mathematical model of generalized thermoelasticity in a fiber-reinforced, isotropic unbounded thermoelastic solid due to the presence of a continuous line heat source under the influence of magnetic field. The derivative is defined in an integral form of a common derivative on a slipping interval by incorporating memory-dependent heat transfer. Employing both Laplace and Hankel transforms as tools, analytical results for distributions of different fields have been derived with the help of potential function approach. The inversion of Hankel transform is performed analytically, whereas the numerical inversion of Laplace transform is carried out employing Zakian method and the method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory to exhibit the significance of the kernel functions and the time-delay parameter is constructed. The significant differences of the two different numerical schemes have also explained. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of reinforcement and magnetic field. Also, significant differences due to the choice of linear and nonlinear kernels in the heat equation is elaborated.

HRV Analysis and Ventricular Arrhythmia Classification using various Classifiers

Ventricular Arrhythmias are one of the fatal heart diseases, requires timely recognition. This paper deals with the classification of some of the ventricular arrhythmias as Premature Ventricular Contraction (PVC), Left Bundle Branch Block (LBBB) and Right Bundle Brach Block (RBBB) with some Normal (N) samples. A Support Vector Machine (SVM), Random Forest and Artificial Neural Network (ANN) classifier was trained and then tested with the help of online available MIT-BIH Arrhythmia Database. Signal processing, generation of Heart Rate Variability (HRV) signals from the available Electrocardiogram (ECG) signals and training and testing of ANN classifier was done in MATLAB environment, and the training and testing of SVM and Random Forest classifier was done in R project software. The SVM classifier was trained with the linear basis function and then with non-linear kernel based function to have better accuracy

Indoor versus outdoor scene recognition for navigation of a micro aerial vehicle using spatial color gist wavelet descriptors

In the context of improved navigation for micro aerial vehicles, a new scene recognition visual descriptor, called spatial color gist wavelet descriptor (SCGWD), is proposed. SCGWD was developed by combining proposed Ohta color-GIST wavelet descriptors with census transform histogram (CENTRIST) spatial pyramid representation descriptors for categorizing indoor versus outdoor scenes. A binary and multiclass support vector machine (SVM) classifier with linear and non-linear kernels was used to classify indoor versus outdoor scenes and indoor scenes, respectively. In this paper, we have also discussed the feature extraction methodology of several, state-of-the-art visual descriptors, and four proposed visual descriptors (Ohta color-GIST descriptors, Ohta color-GIST wavelet descriptors, enhanced Ohta color histogram descriptors, and SCGWDs), in terms of experimental perspectives. The proposed enhanced Ohta color histogram descriptors, Ohta color-GIST descriptors, Ohta color-GIST wavelet descriptors, SCGWD, and state-of-the-art visual descriptors were evaluated, using the Indian Institute of Technology Madras Scene Classification Image Database two, an Indoor-Outdoor Dataset, and the Massachusetts Institute of Technology indoor scene classification dataset [(MIT)-67]. Experimental results showed that the indoor versus outdoor scene recognition algorithm, employing SVM with SCGWDs, produced the highest classification rates (CRs)—95.48% and 99.82% using radial basis function kernel (RBF) kernel and 95.29% and 99.45% using linear kernel for the IITM SCID2 and Indoor-Outdoor datasets, respectively. The lowest CRs—2.08% and 4.92%, respectively—were obtained when RBF and linear kernels were used with the MIT-67 dataset. In addition, higher CRs, precision, recall, and area under the receiver operating characteristic curve values were obtained for the proposed SCGWDs, in comparison with state-of-the-art visual descriptors.

Adaptive data-driven nonlinear synchro squeezed transform with single class radial basis function kernel support vector machine applied to wind turbine planetary gearbox fault diagnostics

Planetary stage gears operated at low rotational speed and varying wind speed result variation in load. Variable speed and variable load induce nonstationary operating conditions. Vibration signal measured from Wind power gear transmission systems are embedded with multiple sources of vibration and attenuated considerably as it travels from source of vibration to measuring point. Efficacious multi-component decomposition without mode mixing ensures the accurate fault signature recognition. Synchro squeezing transform is the promising tool that represents the ridges with high resolution in time as well as in frequency axis. An efficient vibration analysis technique, short windowed Fourier synchro squeezing transform with nonlinear radial basis function kernel support vector machine is proposed to detect the mechanical faults in low speed planetary stage of wind turbines. Raw vibration is modeled in time–frequency plane to extract fault pattern signatures effectively with high resolution by adapting an empirical nonlinear tool synchro squeezing transforms. Amplitude modulation and frequency modulation parameters are sculpted from instantaneous amplitude and instantaneous phase, frequency. Hybrid feature space with signal attributes, statistical moments, and randomness measures are extricated from amplitude modulation-frequency modulation components. Single class radial basis function support vector machine is trained with hybrid features. The fault detection accuracy of the proposed method is compared with the standard variants of empirical mode decomposition. The proposed short windowed Fourier synchro squeezing transform-radial basis function kernel support vector machine shows 98.2% accuracy, 98% sensitivity, and 98% specificity.

Supervised Robust Discrete Multimodal Hashing for Cross-Media Retrieval

The hashing-based approximate nearest neighbors search is able to reduce the storage cost and improve query speed. Therefore, they have attracted much attention in these years. Moreover, some hashing methods have been proposed for cross-modal retrieval tasks. However, there are still some issues that need to be further addressed. For example, some of them only construct a simple similarity matrix when learning hash functions or binary codes, which may lose some useful information. Some of them solve the hard discrete optimization problem by relaxing the binary constraints and quantizing the solution to obtain the final results, which may generate large quantization errors. To address these challenges, we present a new supervised cross-modal hashing method, named supervised robust discrete multimodal hashing (SRDMH). Specifically, it incorporates full label information into the hash functions learning to preserve the similarity in the original space. In addition, instead of relaxing the binary constraints, it is able to learn the binary codes and hash functions simultaneously. Moreover, it adopts a flexible ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,p</sub> loss with nonlinear kernel embedding and introduces an intermediate presentation of the binary codes. In light of this, it becomes more robust and easier to solve by an iterative algorithm presented in this paper. To evaluate its performance, we conduct extensive experiments on three benchmark datasets. The results verify that SRDMH outperforms seven state-of-the-art cross-modal hashing methods. In addition, we also extend it to the classification task. Compared with other hashing methods, SRDMH also obtains better results when its binary codes are used for classification.

Genomic Selection in Rubber Tree Breeding: A Comparison of Models and Methods for Managing G×E Interactions.

Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomic selection (GS) in plant breeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plant breeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomic models and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomic selection (GS) for 435 individual rubber trees at two sites and genotyped the individuals via genotyping-by-sequencing (GBS) of single-nucleotide polymorphisms (SNPs). Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H 2) of 0.60. Applying the model (SM, MM, MDs, and MDe) and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomic models, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS (MM, MDe, or MDs). Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs.

Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes

Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as it is the case for superconducting and charge-density-wave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like non-linear optical kernel. This approach is applied and discussed in few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer an useful perspective to design future experiments in emerging materials.

A unifying view of explicit and implicit feature maps of graph kernels

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.

Deep Kernel for Genomic and Near Infrared Predictions in Multi-environment Breeding Trials.

Kernel methods are flexible and easy to interpret and have been successfully used in genomic-enabled prediction of various plant species. Kernel methods used in genomic prediction comprise the linear genomic best linear unbiased predictor (GBLUP or GB) kernel, and the Gaussian kernel (GK). In general, these kernels have been used with two statistical models: single-environment and genomic × environment (GE) models. Recently near infrared spectroscopy (NIR) has been used as an inexpensive and non-destructive high-throughput phenotyping method for predicting unobserved line performance in plant breeding trials. In this study, we used a non-linear arc-cosine kernel (AK) that emulates deep learning artificial neural networks. We compared AK prediction accuracy with the prediction accuracy of GB and GK kernel methods in four genomic data sets, one of which also includes pedigree and NIR information. Results show that for all four data sets, AK and GK kernels achieved higher prediction accuracy than the linear GB kernel for the single-environment and GE multi-environment models. In addition, AK achieved similar or slightly higher prediction accuracy than the GK kernel. For all data sets, the GE model achieved higher prediction accuracy than the single-environment model. For the data set that includes pedigree, markers and NIR, results show that the NIR wavelength alone achieved lower prediction accuracy than the genomic information alone; however, the pedigree plus NIR information achieved only slightly lower prediction accuracy than the marker plus the NIR high-throughput data.

Hyperspectral Band Selection Using Weighted Kernel Regularization

A band selection method named weighted kernel regularization (WKR) is proposed for hyperspectral imagery (HSI) classification. The WKR aims to select dissimilar and class-separable bands to better model the relationship between labeled samples. First, the WKR considers nonlinear structure of hyperspectral data and models nonlinear relations between HSI samples and their class labels using a weighted kernel ridge regression (WKRR) program with respect to sample coefficients. Second, it combines the L1 penalty term of weights on all bands with the above WKRR program into the unified framework of WKR. The L1 penalty term considers divergent contributions from different bands in describing nonlinear relations and guarantees the sparsity of band weights. Third, the WKR algorithm implements the KerNel Iterative-based Feature Extraction (KNIFE) algorithm to estimate the proper band weights. The KNIFE linearizes the nonlinear kernels to avoid high computational cost, and iteratively minimizes two convex subproblems with respect to the sample coefficients and band weights. Finally, the first k bands with larger weights and larger dissimilarity with other bands are automatically chosen to form the band subset. Experimental results show that the WKR outperforms the state-of-the-art methods in classification accuracies with a lower computational cost.

A re-evaluation of the term spread as a leading indicator

Forecasting the evolution path of macroeconomic variables has always been of keen interest to policy makers and market participants. A common tool used in the relevant forecasting literature is the term spread of Treasury bond yields. In this paper, we decompose the term spread into an expectation and a term premium component and evaluate the informational content of each component in forecasting the GDP growth rate and inflation in various forecasting horizons. In doing so, we employ alternative decomposition procedures and introduce the Support Vector Regression (SVR) methodology from the field of Machine Learning, coupled with linear and non-linear kernels as a novel forecasting method in the field. Using rolling windows in producing point and conditional probability distribution forecasts we find that neither the term spread, nor its decomposition components possess the ability to accurately forecast output growth or inflation. Our findings extend the existing literature, since they are focused on an explicit out-of-sample evaluation in contrast to most existing empirical studies that produce only in-sample forecasts. To strengthen our findings, we also consider several control variables suggested in the relevant literature without significant qualitative differences from the initial results. The main innovation of our approach stems from the use of the non-linear Support Vectors Machine methodology, that is introduced for the first time in this line of research for forecasting out-of-sample.

Unsupervised quadratic surface support vector machine with application to credit risk assessment

Unsupervised classification is a highly important task of machine learning methods. Although achieving great success in supervised classification, support vector machine (SVM) is much less utilized to classify unlabeled data points, which also induces many drawbacks including sensitive to nonlinear kernels and random initializations, high computational cost, unsuitable for imbalanced datasets. In this paper, to utilize the advantages of SVM and overcome the drawbacks of SVM-based clustering methods, we propose a completely new two-stage unsupervised classification method with no initialization: a new unsupervised kernel-free quadratic surface SVM (QSSVM) model is proposed to avoid selecting kernels and related kernel parameters, then a golden-section algorithm is designed to generate the appropriate classifier for balanced and imbalanced data. By studying certain properties of proposed model, a convergent decomposition algorithm is developed to implement this non-covex QSSVM model effectively and efficiently (in terms of computational cost). Numerical tests on artificial and public benchmark data indicate that the proposed unsupervised QSSVM method outperforms well-known clustering methods (including SVM-based and other state-of-the-art methods), particularly in terms of classification accuracy. Moreover, we extend and apply the proposed method to credit risk assessment by incorporating the T-test based feature weights. The promising numerical results on benchmark personal credit data and real-world corporate credit data strongly demonstrate the effectiveness, efficiency and interpretability of proposed method, as well as indicate its significant potential in certain real-world applications.

Extreme learning machines with expectation kernels

Extreme learning machines (ELMs), especially kernel ELMs (KELMs), have achieved great success in providing efficient and effective solutions to classification applications. This paper proposes a simple but effective expectation kernel ELM (EKELM) to improve the classification abilities of ELMs. EKELM is based on a new family of positive semidefinite (PSD) kernel functions, namely expectation kernels (EKs), to learn similarities between data samples by combining the advances of random feature mapping and conventional kernel functions. EK provides a new insight to model ELMs from the perspective of kernel approximation using random sampling techniques. Particularly, we show that the distribution of random sampling weights, i.e. the input weight of ELM, has deep influences on the classification performance, and we use Gaussian distributions to generate random weights in EKELM. Besides, the number of sampling samples, i.e. the number of hidden neurons in ELM, can be reduced by using a proper nonlinear kernel function. We test the proposed EKELM on 20 benchmark classification datasets, the results prove that using a Gaussian distribution to generate random sampling weights has better performance than uniform distribution. Also, the results show that nonlinear RBF EKELM achieves comparable classification performance compared with the conventional RBF kernel, and requires much less random samples compared with linear EKELM.