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The adaptive neurofuzzy inference system (ANFIS) is a structured multioutput learning machine that has been successfully adopted in learning problems without noise or outliers. However, it does not work well for learning problems with noise or outliers. High-accuracy real-time forecasting of traffic flow is extremely difficult due to the effect of noise or outliers from complex traffic conditions. In this study, a novel probabilistic learning system, probabilistic regularized extreme learning machine combined with ANFIS (probabilistic R-ELANFIS), is proposed to capture the correlations among traffic flow data and, thereby, improve the accuracy of traffic flow forecasting. The new learning system adopts a fantastic objective function that minimizes both the mean and the variance of the model bias. The results from an experiment based on real-world traffic flow data showed that, compared with some kernel-based approaches, neural network approaches, and conventional ANFIS learning systems, the proposed probabilistic R-ELANFIS achieves competitive performance in terms of forecasting ability and generalizability.

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles., Comment: The manuscript has been accepted for publication as a regular paper in the IEEE Transactions on Signal Processing

Given a publicly available pool of machine learning models constructed for various tasks, when a user plans to build a model for her own machine learning application, is it possible to build upon models in the pool such that the previous efforts on these existing models can be reused rather than starting from scratch? Here, a grand challenge is how to find models that are helpful for the current application, without accessing the raw training data for the models in the pool. In this paper, we present a two-phase framework. In the upload phase, when a model is uploading into the pool, we construct a reduced kernel mean embedding (RKME) as a specification for the model. Then in the deployment phase, the relatedness of the current task and pre-trained models will be measured based on the value of the RKME specification. Theoretical results and extensive experiments validate the effectiveness of our approach.

Accurate and robust state of charge (SOC) estimation of lithium-ion batteries (LIBs) is very important to prolong battery life and prevent catastrophic failures. However, the accuracy of SOC estimation is seriously affected by unknown noise, uncertain interference and temperature. In this paper, a novel model fusion method is presented to achieve precise SOC estimation in the case of non-Gaussian noise and outliers. A state-space model of battery system is first developed to conduct SOC estimate. Then, a novel robust kernel Takagi Sugeno (T-S) fuzzy method to minimize the mean and variance of model error is developed to characterize the electrical performance of battery. This modeling strategy uses local nonlinear modeling mechanism, which the nonlinear relationship between data can be well represented, thus it can obtain a superior modeling performance. Finally, a multi-innovation unscented Kalman filter (UKF) algorithm considering the historical state information is designed to incorporate with the robust fuzzy model to filter out the noise in the observation and update the SOC estimation. Additional stability analysis shows the convergence of the proposed multi-innovation UKF algorithm. Experiments and verifications show that the presented estimation architecture is effective and has better modeling ability compared with several common methods.

Semisupervised learning (SSL) has been extensively studied in related literature. Despite its success, many existing learning algorithms for semisupervised problems require specific distributional assumptions, such as ``cluster assumption'' and ``low-density assumption,'' and thus, it is often hard to verify them in practice. We are interested in quantifying the effect of SSL based on kernel methods under a misspecified setting. The misspecified setting means that the target function is not contained in a hypothesis space under which some specific learning algorithm works. Practically, this assumption is mild and standard for various kernel-based approaches. Under this misspecified setting, this article makes an attempt to provide a theoretical justification on when and how the unlabeled data can be exploited to improve inference of a learning task. Our theoretical justification is indicated from the viewpoint of the asymptotic variance of our proposed two-step estimation. It is shown that the proposed pointwise nonparametric estimator has a smaller asymptotic variance than the supervised estimator using the labeled data alone. Several simulated experiments are implemented to support our theoretical results.

By training different models and averaging their predictions, the performance of the machine-learning algorithm can be improved. The performance optimization of multiple models is supposed to generalize further data well. This requires the knowledge transfer of generalization information between models. In this article, a multiple kernel mutual learning method based on transfer learning of combined mid-level features is proposed for hyperspectral classification. Three-layer homogenous superpixels are computed on the image formed by PCA, which is used for computing mid-level features. The three mid-level features include: 1) the sparse reconstructed feature; 2) combined mean feature; and 3) uniqueness. The sparse reconstruction feature is obtained by a joint sparse representation model under the constraint of three-scale superpixels' boundaries and regions. The combined mean features are computed with average values of spectra in multilayer superpixels, and the uniqueness is obtained by the superposed manifold ranking values of multilayer superpixels. Next, three kernels of samples in different feature spaces are computed for mutual learning by minimizing the divergence. Then, a combined kernel is constructed to optimize the sample distance measurement and applied by employing SVM training to build classifiers. Experiments are performed on real hyperspectral datasets, and the corresponding results demonstrated that the proposed method can perform significantly better than several state-of-the-art competitive algorithms based on MKL and deep learning.

Asymptotic properties of classical kernel estimators for the spectral density are studied in the locally stationary framework. In particular, it is shown that for a locally stationary process standard spectral density estimators consistently estimate the time-averaged spectral density. This result is complemented by some illustrative examples and applications including HAC-inference in the multiple linear regression model, a simple visual tool for the detection of unconditional heteroskedasticity and a test for covariance stationarity.

Kernel-based models have a strong generalization ability, but most of them, including SVM, are vulnerable to the curse of kernelization. Moreover, their predictive performances are sensitive to the hyperparameters tuning, which highly demands computational resources. These problems render kernel methods problematic when dealing with large-scale datasets. To this end, we first formulate the optimization problem in a kernel-based learning setting as a posterior inference problem, and then develop a rich family of Recurrent Neural Network-based variational inference techniques. Unlike existing literature, which stops at the variational distribution and uses it as the surrogate for the true posterior distribution, here we further leverage Stein Variational Gradient Descent to further bring the variational distribution closer to the true posterior, we refer to this step as Stein Refinement. Putting these altogether, we arrive at a robust and efficient variational learning method for multiclass kernel machines with extremely accurate approximation. Moreover, our formulation enables efficient learning of kernel parameters and hyperparameters which robustifies the proposed method against data uncertainties. The extensive experimental results show that our method, without tuning any parameter, obtains comparable performance to LIBSVM, a well-known implementation of SVM, and outperforms other baselines while being able to seamlessly scale with large-scale datasets.

Binary diffing is a process to discover the patched content between two binary programs. Previous research on binary diffing approach it as a function matching problem to formulate an initial 1:1 mapping between functions, and later a sequence matching ratio is computed to classify two functions being an exact match, a partial match or no-match. The accuracy of existing techniques is best only when detecting exact matches and they are not efficient in detecting partially changed functions; especially those with minor patch. These drawbacks are due to two major challenges (i) In 1:1 mapping phase, using a strict policy to match function features (ii) In classification phase, considering an assembly snippet as a normal text and using sequence matching for similarity comparison. An instruction has a unique structure i.e. mnemonics and registers have specific position in an instruction and also have semantic relationship, which makes assembly code different from general text. Sequence matching performs best for general text but it fail to detect structural and semantic changes at an instruction level thus, its use for classification produces many false results. In this research, we have addressed the aforementioned underlying challenges by proposing a two-fold solution. For 1:1 mapping phase, we have proposed computationally inexpensive features, which are compared with a distance based selection criteria to map the similar functions and filter unmatched functions. For classification phase, we have proposed a Siamese classification embedding neural network where each branch is an attention based distributed learning neural networkthat learn the semantic similarity among assembly instructions, learn to highlight the changes at an instruction level and a final stage fully connected layer learn to accurately classify two 1:1 mapped function either an exact or a partial match. We have used x86 kernel binaries for training and achieved 99% classification accuracy; which is higher than existing binary diffing techniques and tools.

The measurement error evaluation of Power Metering Equipment (PME) is significant for the instrument design and accurate metering of electric energy, especially in extreme environmental stresses. However, actual measurement error prediction is often disturbed by environmental noise and insufficient feature information. To address this problem, an Improved Local Outlier Factor (ILOF) method is first proposed to detect potential outliers. And an optimized distance function and adaptive threshold constraint method based on boxplot are used to improve the outlier detection performance of ILOF. Next, an error prediction method, namely Kernel Support Vector Regression (KSVR), is presented to fuse measurement error and multiple extreme environmental stresses by using the proposed kernel approach. Integrating the ILOF and KSVR, examples from the extreme environmental region demonstrate that the proposed evaluation framework has a higher assessment performance. Compared with several state-of-art prediction methods, our framework has profound outlier identification and error prediction performance under small sample conditions.

In this paper we present a new classification method based on Dictionary Learning (DL). The main contribution consists of a kernel version of incoherent DL, derived from its standard linear counterpart. We also propose an improvement of the AK-SVD algorithm concerning the representation update. Our algorithms are tested on several popular databases of classification problems.

This work examines the impact of multiple vaccination strategies on the dynamics of COVID-19 in a population using the Atangana-Baleanu derivative. The existence and uniqueness of solution of the model is proven using Banach’s fixed point theorem. Local and global asymptotic stability of the equilibria of the model is also proven (under some conditions). Conditions for the existence of a unique or multiple equilibria are also derived and the model is shown to undergo backward bifurcation under certain scenarios. Using available data for the Pfizer, Moderna and Janssen vaccination programme for the city of Texas, United States of America from March 13, 2021 to June 29, 2021, the model is fitted using the three data sets. The three vaccination rates ν 1 , ν 2 and ν 3 corresponding to each vaccine as well as the effective contact rate for COVID-19 transmission, β , are estimated. Simulations of the model under different vaccination strategies are carried out. The results show that the three vaccination strategies not only cause significant reduction in the new asymptomatic and vaccinated symptomatic cases but also cause great decrease in the total number of vaccinated symptomatic individuals with severe COVID-19 illness.

In this paper, we stabilize a discrete-time Markov process evolving on a compact subset of $\mathbb{R}^d$ to an arbitrary target distribution that has an $L^\infty$ density and does not necessarily have a connected support on the state space. We address this problem by stabilizing the corresponding Kolmogorov forward equation, the \textit{mean-field model} of the system, using a density-dependent transition kernel as the control parameter. Our main application of interest is controlling the distribution of a multi-agent system in which each agent evolves according to this discrete-time Markov process. To prevent agent state transitions at the equilibrium distribution, which would potentially waste energy, we show that the Markov process can be constructed in such a way that the operator that pushes forward measures is the identity at the target distribution. In order to achieve this, the transition kernel is defined as a function of the current agent distribution, resulting in a nonlinear Markov process. Moreover, we design the transition kernel to be \textit{decentralized} in the sense that it depends only on the local density measured by each agent. We prove the existence of such

Nowadays, how to select the kernel function and their parameters for ensuring high-performance indicators in fault diagnosis applications remains as two open research issues. This paper provides a comprehensive literature survey of kernel-preprocessing methods in condition monitoring tasks, with emphasis on the procedures for selecting their parameters. Accordingly, twenty kernel optimization criteria and sixteen kernel functions are analyzed. A kernel evaluation framework is further provided for helping in the selection and adjustment of kernel functions. The proposal is validated via a KPCA-based monitoring scheme and two well-known benchmark processes.

This paper concentrates on the $l_{2}-l_{\infty }$ filtering problem of discrete-time fuzzy semi-Markov jump nonlinear system. The random jumps among the studied system are governed by the discrete-time semi-Markov process. Therefore, the storage characteristics of the transition probability between systems are fully considered. To analyze $\sigma$ -mean-square stability of the filtering error system, a filter, which is mode-dependent, based on the discrete-time fuzzy semi-Markov jump model is constructed to estimate the state of the system. Thereafter, based on the Lyapunov stability theory and the discrete-time semi-Markov kernel concept, a set of criteria to ensure the are proposed. In addition, by using Takagi-Sugeno fuzzy model, the nonlinear problem is effectively solved. Ultimately, an illustrative example of a tunnel diode circuit and a numerical example effectively and practicability reveal the developed filtering strategy.

In the paper, a novel kernel recursive least-squares (KRLS) algorithm named random Fourier feature kernel recursive maximum mixture correntropy (RFF-RMMC) algorithm is proposed, which improves the prediction efficiency and robustness of the KRLS algorithm. Random Fourier feature (RFF) method as well as maximum mixture correntropy criterion (MMCC) are combined and applied into KRLS algorithm afterwards. Using RFF to approximate the kernel function in KRLS with a fixed cost can greatly reduce the computational complexity and simultaneously improve the prediction efficiency. In addition, the MMCC maintains the robustness like the maximum correntropy criterion (MCC). More importantly, it can enhance the accuracy of the similarity measurement between predicted and true values by more flexible parameter settings, and then make up for the loss of prediction accuracy caused by RFF to a certain extent. The performance of the RFF-RMMC algorithm for online time series prediction is verified by the simulation results based on three datasets.

Online multiple kernel learning (OMKL) has provided an attractive performance in nonlinear function learning tasks. Leveraging a random feature (RF) approximation, the major drawback of OMKL, known as the curse of dimensionality, has been recently alleviated. These advantages enable RF-based OMKL to be considered in practice. In this article, we introduce a new research problem, named stream-based active MKL (AMKL), in which a learner is allowed to label some selected data from an oracle according to a selection criterion. This is necessary for many real-world applications as acquiring a true label is costly or time consuming. We theoretically prove that the proposed AMKL achieves an optimal sublinear regret O(√T) as in OMKL with little labeled data, implying that the proposed selection criterion indeed avoids unnecessary label requests. Furthermore, we present AMKL with an adaptive kernel selection (named AMKL-AKS) in which irrelevant kernels can be excluded from a kernel dictionary ``on the fly.'' This approach improves the efficiency of active learning and the accuracy of function learning. Via numerical tests with real data sets, we verify the superiority of AMKL-AKS, yielding a similar accuracy performance with OMKL counterpart using a fewer number of labeled data.

The tremendous growth in deep learning (DL) applications has created an exponential demand for computing power, which leads to the rise of AI-specific hardware. Targeted towards accelerating computation-intensive deep learning applications, AI hardware, including but not limited to GPGPU, TPU, ASICs, etc., have been adopted ubiquitously. As a result, domainspecific CAD tools play more and more important roles and have been deeply involved in both the design and compilation stages of modern AI hardware. Recently, ISPD 2020 contest introduced a special challenge targeting at the physical mapping of neural network workloads onto the largest commercial deep learning accelerator, CS-1 Wafer-Scale Engine (WSE). In this paper, we proposed CU.POKer, a high-performance engine fullycustomized for WSE’s DNN workload placement challenge. A provably optimal placeable kernel candidate searching scheme and a data-flow-aware placement tool are developed accordingly to ensure the state-of-the-art quality on the real industrial benchmarks. Experimental results on ISPD 2020 contest evaluation suites demonstrated the superiority of our proposed framework over not only the state-of-the-art (SOTA) placer but also the conventional heuristics used in general floorplanning.

The least-square support vector machine (LS-SVM) has been deeply studied in the machine-learning field and widely applied on a great deal of occasions. A disadvantage is that it is less efficient in dealing with the non-Gaussian noise. In this article, a novel probabilistic LS-SVM is proposed to enhance the modeling reliability even data contaminated by the non-Gaussian noise. The stochastic effect of noise on the kernel function and the regularization parameter is first analyzed and estimated. On the basis of this, a new objective function is constructed under a probabilistic sense. A probabilistic inference method is then developed to construct the distribution of the model parameter, including distribution estimation of both the kernel function and the regularization parameter from data. Using this distribution information, a solving strategy is then developed for this new objective function. Different from the original LS-SVM that uses a deterministic scenario approach to gain the model, the proposed method builds the distribution relation between the model and noise and makes use of this distribution information in the process of modeling; thus, it is more robust for modeling of noise data. The effectiveness of the proposed probabilistic LS-SVM is demonstrated by using both artificial and real cases.

In this article, a general approach for directed graph clustering and two new density-based clustering objectives are presented. First, using an equivalence between the clustering objective functions and a trace maximization expression, the directed graph clustering objectives are converted into the corresponding weighted kernel k-means problems. Then, a nonspectral algorithm, which covers both the direction and weight information of the directed graphs, is thus proposed. Next, with Rayleigh's quotient, the upper and lower bounds of clustering objectives are obtained. After that, we introduce a new definition of weak links to characterize the effectiveness of clustering. Finally, illustrative examples are given to demonstrate effectiveness of the results. This article provides a glance at the potential connection between density-based and pattern-based clustering. Compared with other approaches for directed graph clustering, the method proposed in this article naturally avoids the loss of the nonsymmetric edge data because there is no need for any additional symmetrization.

In this paper, we present generalized Jensen-Mercer inequality for a generalized h-convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h-convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature.

A key energy consumption in steel metallurgy comes from an iron ore sintering process. Enhancing carbon utilization in this process is important for green manufacturing and energy saving and its prerequisite is a time-series prediction of carbon efficiency. The existing carbon efficiency models usually have a complex structure, leading to a time-consuming training process. In addition, a complete retraining process will be encountered if the models are inaccurate or data change. Analyzing the complex characteristics of the sintering process, we develop an original prediction framework, that is, a weighted kernel-based fuzzy C-means (WKFCM)-based broad learning model (BLM), to achieve fast and effective carbon efficiency modeling. First, sintering parameters affecting carbon efficiency are determined, following the sintering process mechanism. Next, WKFCM clustering is first presented for the identification of multiple operating conditions to better reflect the system dynamics of this process. Then, the BLM is built under each operating condition. Finally, a nearest neighbor criterion is used to determine which BLM is invoked for the time-series prediction of carbon efficiency. Experimental results using actual run data exhibit that, compared with other prediction models, the developed model can more accurately and efficiently achieve the time-series prediction of carbon efficiency. Furthermore, the developed model can also be used for the efficient and effective modeling of other industrial processes due to its flexible structure.

This paper develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this paper we construct a multi-kernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multi-kernel algorithm and its rate of convergence. In numerical examples, we study the multi-kernel version of the passive least mean squares (LMS) algorithm for transfer learning to compare the performance with the classical passive version.

Feature selection is of great importance to make prediction for process variables in industrial production. An embedded feature selection method, based on relevance vector machines with an approximated marginal likelihood function, is proposed in this study. By setting hierarchical prior distributions over the model weights and the parameters of the automatic relevance determination kernel function, respectively, a Gaussian approximation method is designed to approximate the intractable exact marginal likelihood by using the law of the total expectation and the total covariance. Furthermore, in this study, the joint posterior distribution over the model weights and the kernel parameters is estimated by combining the Gibbs sampling with a Laplace approximation. Thus, feature selection is performed by examining the posterior over the kernel parameters. To verify the performance of the proposed method, a series of benchmark datasets and two practical industrial datasets are employed. The experimental results demonstrate that the proposed method not only produces higher prediction accuracy than other methods but also performs better in feature selection, especially in industrial case.

A mathematical model describing the HIV/AIDS transmission dynamics in the existence of an aware community using fractional differential operator having Mittag–Leffler kernel is presented and investigated in this paper. By using the fixed point theorem, the existence and uniqueness conditions of the model are obtained. We have used a novel technique known as the iterative Laplace transform approach to obtain the approximate solution of the mathematical model of HIV/AIDS based on the Atagana-Baleanu operator.We investigate the necessary conditions for the disease control in order to determine the role of unaware infective in the spread of HIV/AIDS. The numerical simulations and plots are demonstrated for different values of fractional order. Moreover, we have compared the obtained numerical results based on the Atagana-Baleanu operator with the values obtained using the Caputo operator for the suggested model. We believe that Atangana-Baleanue fractional derivative and the suggested algorithm are expected to be used in future to formulate and analyse many generalised fractional models.

Kernel size, one of the traits that determine wheat yield, is controlled by multiple quantitative trait loci. Polish wheat (Triticum polonicum) has elongated and plump kernel and is a valuable material for breeding high-yielding wheat cultivars. However, genes or loci determining kernel length (KL) in Polish wheat are unknown. We identified and validated a major KL gene, KL-PW, at the P1 locus in Polish wheat. KL-PW is VRT-A2, which encodes a MIKC-type MADS-box protein (MADS55). An insertion/deletion mutation in intron 1 of VRT-A2PW led to an alternatively spliced transcript, VRT-A2PW2. Quantitative PCR analysis showed that VRT-A2PW was more highly expressed in developing seeds than was VRT-A2Ailanmai. Brassinosteroid (BR) sensitivity experiment and the expression of BR-related genes indicated that VRT-A2PW functions as a positive regulator of BR responses. VRT-A2PW significantly increased KL of wheat. These findings not only reveal the molecular basis of KL-PW in controlling KL, but also provide a valuable genetic resource for increasing kernel size in wheat.

Computer-assisted pathology analysis is an emerging field in health informatics and extremely important for effective treatment. Herein, we demonstrated the ability of the pre-trained Xception model for magnification-dependent breast cancer histopathological image classification in contrast to handcrafted approaches. The Xception model and SVM classifier with the ‘radial basis function’ kernel has achieved the best and consistent performance with the accuracy of 96.25%, 96.25%, 95.74%, and 94.11% for 40X, 100X, 200X and 400X level of magnification, respectively. A comparison with existing state-of-the-art techniques has been conducted based on accuracy, recall, precision, F1 score, area under ROC and precision–recall curve evaluation metrics.

In this article, we presented a nonlinear time-fractional mathematical model of the Ebola Virus in order to understand the outbreak of this epidemic disease. Ebola virus is a highly contagious disease that can be spread in the population depending upon the number of individuals and their dynamics in the community. The Caputo and Atangana Baleanu fractional derivative operators are employed to get the solution of the system of fractional differential equations. The qualitative analysis has been made for the fractional-order model. Fixed-point theorem and an iterative schemes are used to get the existence and uniqueness. The actual behavior of the time-fractional model has been obtained by employing Laplace Adomian Decomposition technique. Finally, numerical results have been established for the system of fractional differential equations with simulations to demonstrate the impacts of the fractional-order parameters on the proposed system to achieve the theoretical outcomes and a comparison has been made with the Caputo for better analysis.

This paper is concerned with the mode-dependent sliding mode control (SMC) for uncertain discrete-time semi-Markov switching systems (S-MSSs). The switching is governed by a semi-Markov chain with a discrete-time semi-Markov kernel (SMK). First, a sliding mode surface (SMS) is constructed to be related to the current switching mode. Second, by means of the upper bound of the sojourn time (ST), some feasible conditions are derived to guarantee σ-error mean square stability for the corresponding S-MSSs. Third, an appropriate SMC law is established to drive the state onto the specified sliding domain. Finally, an F-404 aircraft model validates the proposed control algorithm.

There are two types of important information in a polarimetric synthetic aperture radar (PolSAR) image: spatial features in two dimensions and polarimetric characteristics in the scattering dimension. Considering both polarimetric and spatial information is important for PolSAR image classification. Convolutional kernels show superior performance for extraction of spatial information from two dimensions of an image in convolutional neural networks (CNNs). But learning CNNs needs large enough training sets to achieve the optimum weights of kernels while there are not usually sufficient training samples for PolSAR images. To deal with this difficulty, a convolutional kernel‐based covariance descriptor (CKCD) is introduced for PolSAR image classification in this study. To extract contextual characteristics, compatible with the original image, the fixed‐valued convolutional kernels randomly selected from the image are used, which do not require any learning, and so do not need any training samples. To include more local spatial information and find the relation among the polarimetric features, the covariance descriptor is constructed on the extracted feature maps. Then, the polarimetric‐contextual features are given to a support vector machine with a matrix logarithm‐based kernel. Finally, the guided filter is applied to the initial classification map to result a smoothed classification map with preserved edges. The experiments on three real PolSAR images show superiority of the proposed CKCD method compared to several PolSAR classification methods such as 2DCNN and 3DCNN in small sample size situations.

One-class classification achieves anomaly/outlier detection by exploiting the characteristics of target data. As a local similarity measure defined in kernel space, correntropy is generally more robust than the mean square error (MSE) based criterion in dealing with large outliers. In this paper, the maximum mixture correntropy criterion (MMCC) with multiple kernels are applied to the shallow and hierarchical one-class extreme learning machine (OC-ELM) to enhance the model robustness and learning speed. Experiments on benchmark UCI classification datasets, urban acoustic classification (UAC) dataset and 4 synthetic datasets are carried out to show the effectiveness and comparisons with several state-of-the-art methods are provided to demonstrate the superiority of the proposed algorithms.

The point of this paper is to analyze and investigate the analytic-approximate solutions for fractional system of Volterra integro-differential equations in framework of Caputo-Fabrizio operator. The methodology relies on creating the reproducing kernel functions to gain analytical solutions in a uniform form of a rapidly convergent series in the Hilbert space. Using the Gram-Schmidt orthonomalization process, the orthonormal basis system is constructed in a dense compact domain to encompass the Fourier series expansion in view of reproducing kernel properties. Besides, convergence and error analysis of the proposed technique are discussed. For this purpose, several numerical examples are tested to demonstrate the great feasibility and efficiency of the present method and to support theoretical aspect as well. From a numerical point of view, the acquired solutions simulation indicates that the methodology used is sound, straightforward, and appropriate to deal with many physical issues in light of Caputo-Fabrizio derivatives.

The constant kernel width of generalized maximum correntropy criteria (GMCC) has arisen that the steady-state error and convergence speed can be mutually exclusive. To solve this problem, this paper proposes the variable kernel width (VKW) GMCC algorithm. Actually, due to the censored problem, the output data value beyond the limit of the recording device can not be well observed. In this case, we further developed a variable kernel width GMCC algorithm based on censored regression (CRVKWGMCC). Simulation results show that the proposed CR-VKWGMCC algorithm has excellent performance in both Gaussian and non Gaussian noise.

The present study provided the first-time comprehensive evaluation of 12 advanced statistical and machine learning (ML) algorithms for the Soil Moisture (SM) estimation from dual polarimetric Sentinel-1 radar backscatter. The ML algorithms namely support vector machine (SVM) with linear, polynomial, radial and sigmoid kernel, random forest (RF), multi-layer perceptron (MLP), radial basis function (RBF), Wang and Mendel’s (WM), subtractive clustering (SBC), adaptive neuro fuzzy inference system (ANFIS), hybrid fuzzy interference system (HyFIS), and dynamic evolving neural fuzzy inference system (DENFIS) were used. Extensive field samplings were performed for collection of in-situ SM data and other parameters from the selected sites for seven different dates and at two different locations (Varanasi and Guntur District, India), concurrent to Sentinel-1 overpasses. The backscattering coefficients were considered as input variables and SM as output variable for the training, validation and testing of the ML algorithms. The site at Varanasi was used for the training, validation and testing of the models. On the other hand, the Guntur site was used as an independent site for checking the model performance, before finalizing the algorithms. The performances of different trained algorithms were evaluated in terms of correlation coefficient (r), root mean square error (RMSE) (in m3/m3) and bias (in m3/m3). The study identified the RF, SBC and ANFIS as the top three best performing models with comparable and promising SM estimation. In order to test the robustness of these best models (RF, SBC and ANFIS), further performance analysis was performed to the independent datasets of the Varanasi and Guntur test sites, which indicates that the performance of these three models were consistent and SBC can be recommended as the best among all for SM estimation.

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is a complex combinatorial optimization problem for which finding high quality feasible solutions is very challenging. Recently, several heuristic approaches and a few exact algorithms have been proposed for its solution. These methods have been able to provide new best-known values for benchmark instances although many of them still remain unclosed to optimality. In this paper, we provide a new variant of the heuristic framework Kernel Search and apply it to the MMKP. The proposed variant keeps the method’s main idea of solving a sequence of restricted mixed-integer subproblems but innovates by partitioning the solution process into two different phases with complementary goals. The first phase strives for feasibility and collects important information to dynamically adapt subproblems’ dimension and solution time in the second phase that is focused on getting high quality solutions. This makes the global approach more scalable and efficient. Computational results on different sets of benchmark instances demonstrate that our method is extremely effective outperforming all state-of-the-art heuristics for the MMKP. The method compares extremely well also with respect to exact approaches running for five hours. The proposed algorithm is able to improve the best-known value of 185 out of 276 open benchmark instances and gets 8 out of 17 optimal solutions for the closed ones. The average deviation from optimality is always negligible.

Typical online learning methods have brought fruitful achievements based on the framework of online convex optimization. Meanwhile, nonconvex loss functions also received numerous attentions for their merits of noise-resiliency and sparsity. Current nonconvex loss functions are typically designed as smooth for the ease of designing the optimization algorithms. However, these loss functions no longer have the property of sparse support vectors. In this work, we focus on regression with a special type of nonconvex loss function (i.e., canal loss), and propose a kernel-based online regression algorithm, n oise- r esilient o nline r egression (NROR), to deal with the noisy labels. The canal loss is a type of horizontally truncated loss and has the merit of sparsity. Although the canal loss is nonconvex and nonsmooth, the regularized canal loss has a property similar to convexity which is called strong pseudo-convexity. Furthermore, the sublinear regret bound of NROR is proved under certain assumptions. Experimental studies show that NROR achieves low prediction errors in terms of mean absolute error and root mean squared error on the datasets of heavy noisy labels. Particularly, we check whether the convergence assumption strictly holds in practice and find that the assumptions required for convergence are rarely violated, and the convergence rate is not affected.

Regional as well as global cropland database at a high spatial resolution like 10 m is not available. This study aims to integrate the Sentinel-1 synthetic aperture radar (SAR) data and Sentinel-2 optical data in a more robust way to map the croplands at 10 m spatial resolution. It also examines the effectiveness of different derived products from the SAR and multispectral data. The VH and VV polarizations of the SAR data were used to generate the 80 textural parameters at four different kernel sizes. The multispectral bands of the optical data were used to create nine different spectral indices. The SAR and optical data were classified separately and integrated with the other derived products, using the random forest classifier, to identify the most potential way to use the two datasets for LULC classification. The classification accuracy was the least when only the Sentinel 1 data was used, with an overall accuracy of 59.48% and a kappa value of 0.51. The best accuracy (97.94% overall accuracy and 0.98 kappa value) was achieved by combining the Sentinel 1 and 2 data and their optimal textures and spectral indices. Overall, this study suggests the suitability of the SAR data along with optical data to map the croplands with higher accuracy.

OpenCL programs typically employ complex storage models and diverse data types as well as manifest various memory access patterns, which make it challenging to detect the performance problems effectively. However, few research efforts have been dedicated to cope with this challenge so far. In this paper, we introduce CVFuzz, a domain-independent tool that can effectively detect and locate algorithmic complexity vulnerabilities in OpenCL kernels. The key enabling idea is leveraging automatically generated pathological inputs to trigger the worst-case behavior during the execution of OpenCL kernels. Our approach takes advantage of the metrics such as code coverage and run time to guide the generation of inputs that can slow down the execution of a given OpenCL kernel. We evaluate CVFuzz on more than 250 real-world OpenCL kernels. The evaluation results demonstrate that the inputs generated by CVFuzz are effective in detecting the worst-case time algorithmic complexity and optimization vulnerabilities.

Spatially explicit measurement of Above Ground Biomass (AGB) is crucial for the quantification of forest carbon stock and fluxes. To achieve this, an integration of Optical and Synthetic Aperture Radar (SAR) satellite datasets could provide an accurate estimation of forest biomass. This will also help in removing the uncertainties associated with the single sensor-based estimation approaches. Therefore, the present study attempts to integrate Sentinel-2 optical data with Sentinel-1 SAR dataset to estimate AGB in the Shoolpaneshwar Wildlife Sanctuary (SWS), Gujarat, India. In this study, two non-parametric machine learning algorithms viz Support Vector Machines (SVMs) with different kernel functions—linear, sigmoidal, radial and polynomial and Random Forest (RF) were employed for the prediction of AGB using different combinations of VV, VH, Normalized Difference Vegetation Index (NDVI) and Incidence Angle (IA). Ground based AGB was estimated through allometric equation at 35 sampling sites with the help of tree height and Diameter at Breast’s Height (DBH). Standalone collinearity analysis among different parameters resulted in poor correlation of AGB with VH (r = 0.05) and IA (r = 0.015), whereas a significantly good correlation with NDVI (r = 0.80) and VV (r = 0.74) were observed. Inclusion of NDVI with VV and VH together also resulted in a better correlation (r = 0.85) than other combinations. The SVM with linear kernel utilizing parametric the combinations of VV + VH + NDVI and VV + VH + NDVI + IA were found to be best performing on the basis of evaluation metrics. The outcome of this study highlighted the significance of machine learning techniques and synergistic use of different remote sensing data for an improved AGB quantification in tropical forests.

Background Brain network describing interconnections between brain regions contains abundant topological information. It is a challenge for the existing statistical methods (e.g., t test) to investigate the topological differences of brain networks. Methods We propose a kernel based statistic framework for identifying topological differences in brain networks. In our framework, the topological similarities between paired brain networks are measured by graph kernels. Then, graph kernels are embedded into maximum mean discrepancy for calculating kernel based test statistic. Based on this test statistic, we adopt conditional Monte Carlo simulation to compute the statistical significance (i.e., p value) and statistical power. We recruited 33 patients with Alzheimer's disease (AD), 33 patients with early mild cognitive impairment (EMCI), 33 patients with late mild cognitive impairment (LMCI) and 33 normal controls (NC) in our experiment. There are no statistical differences in demographic information between patients and NC. The compared state-of-the-art statistical methods include t test, t squared test, two-sample permutation test and non-normal test. Results We apply the proposed shortest path matched kernel to our framework for investigating the statistical differences of shortest path topological structures in brain networks of AD and NC. We compare our method with the existing state-of-the-art statistical methods in brain network characteristic including clustering coefficient and functional connection among EMCI, LMCI, AD, and NC. The results indicate that our framework can capture the statistically discriminative shortest path topological structures, such as shortest path from right rolandic operculum to right supplementary motor area (p=0.00314, statistical power=0.803). In clustering coefficient and functional connection, our framework outperforms the state-of-the-art statistical methods, such as p=0.0013 and statistical power=0.83 in the analysis of AD and NC. Conclusion Our proposed kernel based statistic framework not only can be used to investigate the topological differences of brain network, but also can be used to investigate the static characteristics (e.g., clustering coefficient and functional connection) of brain network.

Influenza poses a significant risk to public health, as evidenced by the 2009 H1N1 pandemic which caused up to 203,000 deaths worldwide. Predicting the spatiotemporal information of disease in the incubation period is crucial because the prime aim of it is to provide guidance on preparing a response and avoid presumably adverse impact caused by a pandemic. This article designs and analyzes a prediction system about influenza-like illness (ILI) from the latent temporal and spatial information. In this system 1) Gaussian function model and multivariate polynomial regression are employed to investigate the temporal and spatial distribution of ILI data; 2) the phase space reconstructed by delay-coordinate embedding is used to explore the dynamical evolution behavior of the 1-D ILI series; and 3) a dynamical radial basis function neural network (DRBFNN) method which is the kernel of the system, is proposed to predict the ILI values based on the correlations between the observations space and reconstructed phase space. The performance analysis of our system shows that the regression equations coupling with spatial distribution information can be used to supplement the missing data, and the proposed DRBFNN method can predict the trends of ILI for the following one year. Furthermore, the prediction system in this article applies a model-free control schemes, i.e., there are no restriction equations between the multivariable inputs and outputs. This prediction system is expected to be used in predicting the output signals, even the chaotic output signals, in meteorology, industry, medicine, economy, and other fields. An example of predicting the Standard & Poors 500 index is given to introduce the application of our proposed system. The trend of open prices of the following eight trading days is well predicted.

Bidirectional reflectance distribution function (BRDF) models are used to correct surface bidirectional effects and estimate land surface albedo. Many operational BRDF/albedo algorithms adopt a Roujean linear kernel-driven BRDF (RLKB) model because of its simple form and good performance in fitting multidirectional surface reflectance values. However, this model does not explicitly consider topographic effects, resulting in errors when applied over rugged terrain. To address this issue, we proposed a hybrid algorithm suitable for both flat and rugged terrain, called topographical kernel-driven (Topo-KD). First, we constructed a linear kernel-driven BRDF model considering terrain (LKB_T) which describes the topographic effects with a mountain radiative transfer (MRT) model. Then, the Topo-KD algorithm adaptively selects the most suitable model (RLKB or LKB_T) according to the terrain conditions and fitting residuals. The performances of Topo-KD and RLKB using the RossThick-LiSparseReciprocal (RTLSR) kernel are compared using simulated data sets and moderate-resolution imaging spectroradiometer (MODIS) observations. The results show that the BRDF of the pixel is affected by topography. But the RTLSR model does not specifically account for it, resulting in larger biases over rugged terrain than the Topo-KD algorithm in both the red and near-infrared (NIR) bands. The experiment using MODIS data sets demonstrates that the Topo-KD algorithm reduces fitting residuals in the red and NIR bands by 21.5% and 27.4% compared with the RTLSR model. These results indicate that the Topo-KD algorithm can be a better choice for retrieving land surface parameters and describing the radiative transfer process in mountainous areas.

A latent function decomposition method is proposed for forecasting the capacity of lithium-ion battery cells. The method uses the multioutput convolved Gaussian process (MCGP), a machine learning framework for multitask and transfer learning. The MCGP decomposes the available capacity trends from multiple battery cells into latent functions. The latent functions are then convolved with optimized kernel smoothers to reconstruct and forecast the capacity trends. The latent functions capture nontrivial cross correlations between the capacity trends of the available battery cells. The MCGP also provides uncertainty quantification for its predictions. These two merits make the proposed MCGP a very reliable and practical solution for applications that use battery cell packs. The MCGP is derived and compared to benchmark methods on two experimental lithium-ion battery cells datasets. The results show the effectiveness of the proposed MCGP for long-term capacity forecasting.

One fundamental task of hyperspectral imaging is spectral unmixing. In this case, the conventional pure pixel-based hyperspectral image classification (HSIC) may not work effectively for mixed pixels. This article presents a kernel-based approach to hyperspectral mixed pixel classification (HMPC) which includes two nonlinear mixed pixel classifiers, kernel constrained energy minimization (KCEM) and kernel linearly constrained minimum variance (KLCMV) to replace the widely used pure pixel-based support vector machine (SVM) classifier. Interestingly, what the binary-class and multiclass SVM classifiers are to pure pixel-based HSIC can be similarly derived for what a single-class KCEM detector and a multiclass KLCMV detector are to HMPC. In particular, the commonly used discrete classification map-based hard classification measures, average accuracy (AA) and overall accuracy (OA) for performance evaluation can be further generalized to real-valued mixed class abundance fractional map-based soft classification measures via 3-D receiver operating characteristic (3-D ROC) analysis-derived detection measures. Extensive experiments are conducted to demonstrate the utility of HMPC where KCEM/KLCMV not only significantly improve the classification performance of CEM/LCMV-based classifiers but also outperform many existing spectral-spatial classification methods.

The kernel principal component analysis (KPCA) is widely used as a fault monitoring tool for complex nonlinear chemical processes in recent years. The cumulative contribution rate that extracts the kernel principal is usually obtained relied on a fixed model, which cannot be employed for time-varying chemical processes. Hence, a novel adaptive kernel principal component analysis (AKPCA) integrating grey relational analysis (GRA) (AKPCA-GRA) is proposed to dynamically monitor the fault occurrence. A moving window integrating the threshold method is used to adaptively extract the kernel principal for chemical processes. Then the corresponding T2 and Q statistics calculated by the selected kernel principal based on the AKPCA decides whether the fault has occurred. Moreover, the GRA method is used to analyze and calculate the correlation coefficient of abnormal features obtained based on the APKCA method, which provides the operational guidance for the nonlinear chemical process to find out the variable causing the fault. Finally, the proposed method is verified using the Tennessee Eastman (TE) process. The case results demonstrate that the proposed method outperforms the KPCA, the KPCA based on the threshold and the moving window principal component analysis, the support vector machine (SVM) and the Logistic Regression (LR) in terms of the missed alarm rate (MAR) and the false alarm rate (FAR), which can effectively analyze the variables causing the fault.

This paper concerns the problem of boundary time-varying feedback controller for fixed-time stabilization of a linear parabolic distributed parameter system with spatially and temporally varying reactivity. By utilizing the continuous backstepping approach, the invertible Volterra integral transformation with the time-dependent gain kernel is introduced to convert the closed-loop system into a target system with a time-dependent coefficient. Meanwhile, the convergence of the target system within the prescribed time is guaranteed via the Lyapunov method. The well-posedness of the resulting kernel partial differential equations is also proven by exploiting the method of successive approximation. In addition, the growth-in-time of the kernel functions is estimated by applying the generalized Laguerre polynomials and the modified Bessel functions. Subsequently, the fixed-time stability of the closed-loop system under state feedback control within the prescribed time is proven by using the fixed-time stability of the target system and the time-varying kernel functions. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control method.