Robust Kernel Research Articles

Prediction of thermal conductivity and damage in Indian Jalore granite for design of underground research laboratory

The measurement of thermal conductivity of granitic rocks is a time-consuming process and requires highly sophisticated instruments for experimental analysis. The difficulties in proposing reliable and precise empirical correlations and theoretical models forced the researchers to use alternative and more accurate models based on artificial intelligence (AI) techniques. The present study has been carried out to predict two parameters, thermal conductivity, and damage threshold for Jalore granite using AI techniques. In this study, artificial neural networks (ANNs), linear regression, support vector regressors (SVRs),, and decision tree regressors (DTRs) have been applied to obtain reliable and more accurate models. The extensive analysis revealed that the optimum performance is obtained by the ANN model with 8 nodes in the input layer with 2 hidden layers. Hidden layers having 15 and 7 nodes in the first and second layers, respectively. Softmax function has been applied as activation for each layer of the developed model. The mean absolute error (MAE) and mean squared error (MSE) values for the model while predicting the thermal coefficient were 0.0033671 and 184E−05. These values were 0.0016141 and 3.89E−06 for the damage threshold. DTRs with the number of estimators, n = 100, 1000, and 10,000 perform relatively well for predicting the values for both parameters. Linear regression and SVRs models (linear and robust kernel) show some deviations from the observed values at points where the trend shows a sudden change or kink. In the case of DTRs, the model with the number of estimators, n = 1000, and 100 performs most efficiently for predicting thermal conductivity (MSE = 6.81E−05) and the damage threshold (MSE = 2.84E−05), respectively.

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.

Adaptive Robust Kernels for Non-Linear Least Squares Problems

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels as the standard way for dealing with outliers in the data. These kernels, however, are often hand-picked, sometimes in different combinations, and their parameters need to be tuned manually for a particular problem. In this letter, we propose the use of a generalized robust kernel family, which is automatically tuned based on the distribution of the residuals and includes the common m-estimators. We tested our adaptive kernel with two popular estimation problems in robotics, namely ICP and bundle adjustment. The experiments presented in this letter suggest that our approach provides higher robustness while avoiding a manual tuning of the kernel parameters.

Marginalizing Sample Consensus.

A new method for robust estimation, MAGSAC++, is proposed. It introduces a new model quality (scoring) function that does not make inlier-outlier decisions, and a novel marginalization procedure formulated as an M-estimation with a novel class of M-estimators (a robust kernel) solved by an iteratively re-weighted least squares procedure. Instead of the inlier-outlier threshold, it requires only its loose upper bound which can be chosen from a significantly wider range. Also, we propose a new termination criterion and a technique for selecting a set of inliers in a data-driven manner as a post-processing step after the robust estimation finishes. On a number of publicly available real-world datasets for homography, fundamental matrix fitting and relative pose, MAGSAC++ produces results superior to the state-of-the-art robust methods. It is more geometrically accurate, fails fewer times, and it is often faster. It is shown that MAGSAC++ is significantly less sensitive to the setting of the threshold upper bound than the other state-of-the-art algorithms to the inlier-outlier threshold. Therefore, it is easier to be applied to unseen problems and scenes without acquiring information by hand about the setting of the inlier-outlier threshold. The source code and examples both in C++ and Python are available at https://github.com/danini/magsac.

Robust Kernel Correlation Based Bi-Channel Signal Detection With Correlated Non-Gaussian Noise

This letter proposes a robust detector based on kernel correlation (KC) for detecting the presence of a common random signal shared in two channels corrupted by correlated non-Gaussian impulsive noise. A bivariate Gaussian mixture (GM) distribution is employed to simulate the correlation and impulsive characteristic of the noise across two channels. The test statistic is constructed by the dot product of preprocessed data obtained by imposing the nonlinear Gaussian kernel on the original observed samples from the two channels. Performance metrics with respect to the probabilities of false alarm and detection are established in view of the central limit theorem (CLT). Simulation results illustrated that, in terms of receiver operating characteristic (ROC) curve and detection probability, the proposed method is superior to other state-of-the-art detection algorithms in the literature.

A variable-scale S-type kernel fractional low-power adaptive filtering algorithm

The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.

Fault Detection of Wind Turbines by Subspace Reconstruction-Based Robust Kernel Principal Component Analysis

Data collected from the supervisory control and data acquisition (SCADA) system are widely used in wind farms to detect wind turbines’ (WTs) faults. However, it is challenging to extract wind turbines’ performance trends and provide accurate alarms based on SCADA data with large operating conditions fluctuations. This article presents a fault detection frame of subspace reconstruction-based robust kernel principal component analysis (SR-RKPCA) model for wind turbines SCADA data to extract nonlinear features under discontinuous interference. First, to improve the stability of the fault detection model of wind turbines, an RKPCA method is developed to decompose the original signal, decomposed into principal component subspace and residual subspace. Second, the permutation entropy is adopted to measure the residual matrix components’ disturbance level and remove trendless noise components. Then, a combined index is developed for fault detection with the aid of the residual space matrix with trend information. Ultimately, the proposed SR-RKPCA method for wind turbine detection is verified by investigating wind turbine faults cases. The proposed method has outstanding robustness and a more vital ability to extract nonlinear features for fault detection than traditional principal component analysis (PCA)- or KPCA-based methods.

Nonuniform blind deblurring for single images based on adaptive edge-enhanced regularization

Natural images inevitably suffer from spatially variant blur caused by the relative motion between a camera and objects. We present an effective and efficient patch-wise edge-enhanced image regularization and a robust kernel similarity constraint to perform an accurate kernel estimation from coarse-to-fine iterations. The proposed adaptive regularization introduces a gradient magnitude penalty function into total variation to preserve and enhance salient edges while smoothing out harmful subtle structures. In addition, the similarity constraint is engaged in each patch without camera rotation effects, ensuring that the erroneous kernels can be identified by measuring the similarity among the kernels of neighbor patches and be replaced with the well-estimated ones. After obtaining accurate kernels, numerous nonblind deblurring methods can be applied to restore an image. Numerical experiments demonstrate that the proposed algorithm performs favorably without ringing artifacts and possesses high processing efficiency for natural nonuniform blurred images.

A lifecycle operating performance assessment framework for hot strip mill process based on robust kernel canonical variable analysis

In the modern hot strip mill process (HSMP), the operating performance may deteriorate because of wear of equipment, mode transitions, and random disturbances. If the process is not adjusted and maintained, faults may occur, resulting in greater economic losses and potential safety hazards. Therefore, it is of great practical significance to carry out comprehensive operating performance assessment. In this paper, a lifecycle operating performance assessment framework based on robust kernel canonical variable analysis (RKCVA) is proposed to deal with automation hierarchy, nonlinearity, and outliers in the plant-wide HSMP. First, the HSMP is divided into upstream, midstream, and downstream in real-time control level (L1). Then, based on kernel canonical variable analysis (KCVA) and partial robust M-regression (PRM), the RKCVA models are developed for each stream and process control level (L2). Based on the Bayesian inference, statistical fusion is implemented to judge whether the process is in normal or faulty operating condition. After that, according to different evaluation rules of different operating conditions, the lifecycle operating performance assessment is realized. Finally, the framework is illustrated with a case study on a real HSMP. The assessment results show that the accuracy of the RKCVA is more than 10% higher than that of the KCVA.

Blind deconvolution via complementarily structure-aware image smoothing

Blind deconvolution is known as a challenging low-level vision problem due to the diverse blur scenarios in real-world imaging. Another attempt is made with critical thoughts on existing image priors for nonparametric blur kernel estimation, proposing an alternative approach to blind deconvolution via complementarily structure-aware image smoothing (CSIS). Similar to most state-of-the-art blind deblurring methods, the proposed approach partly builds on the naive L0-based sparse model, but the core contribution here is to additionally advocate a type of redescending potential (RDP) functions as a more elegant way for boosting blind deblurring. With the RDP element, the new approach is capable of easily achieving the discrimination between clear and blurred images. Meanwhile, the performance of the proposed method can be better ensured due to the complementary smoothing behavior induced by the RDP functions. Specifically speaking, it is known that L0-based smoothing plays a critical role in pursuing salient step-edges from blurry images especially in the early period of blur kernel estimation, whereas the RDP-based smoothing is found particularly significant in the later stage when the fine pursuit of salient roof-edges or ramp-edges are dominantly critical for more precise and robust kernel estimation. In this sense, the proposed CSIS-based blind deblurring algorithm is more intuitive than previous L0-based methods. Not only that, numerous experimental results on benchmark blurred images, no matter synthetic or realistic, also demonstrate the comparable or even better performance of the proposed approach in terms of both effectiveness and robustness.

Data-driven robust day-ahead unit commitment model for hydro/thermal/wind/photovoltaic/nuclear power systems

According to the complementary characteristics of various power sources, this paper establishes a data-driven robust day-ahead unit commitment model for a hydro-thermal-wind-photovoltaic-nuclear power system that can be used by the independent system operaters (ISOs). A data-driven robust optimization method based on the robust kernel density estimation (RKDE) is employed to deal with the uncertainties of wind and photovoltaic (PV) power. That is, the distributional information of wind and PV power is extracted by RKDE from the big data, then it is incorporated into the data-driven uncertainty set, and finally a robust optimization model is formed. In view of the facts that the conventional water spillage methods fail to pay equal attention to the benefits of the basin and the individual hydro plants, eight kinds of strategies that can make the water spillages or hydropower curtailments distributed proportionally in each hydro plant are proposed. In addition, the operating model of nuclear power unit involved in peak load regulation is established to promote its operational flexibility. The numerical results and simulation on a modified New England 39-bus system verify the superiority and practicability of the proposed model.

Research on a factor graph-based robust UWB positioning algorithm in NLOS environments

In a non-line-of-sight (NLOS) environment, ultra-wide band (UWB) high accuracy positioning has been one of the hot topics in studying indoor positioning. In this paper, a factor graph-based UWB positioning algorithm has been proposed based on an improved Turkey robust kernel. It has overcome not only the defect of the least squares algorithm for UWB positioning against non-Gaussian noise but also eliminated the shortcoming of Turkey robust kernel against over-optimization. Aiming at the character of UWB data generally larger than its true value due to barriers, robust kernel will be added into merely big ranging data. However, due to the presence of small ranging data possibly caused by error positioning, the squares of residuals will be taken as the optimized objective function. The experimental result proves that UWB positioning algorithm based on the improved Turkey robust kernel outperforms ordinary UWB positioning algorithms in NLOS environments, with the average positioning accuracy improved by around 20–30%.

Towards smart transportation: A learning‐based data‐driven optimization approach for electric taxi dispatch problem

Electric taxi dispatch problem (ETDP) is one of the key issues in smart transportation. Existing study in the context of centralized optimization adopts either deterministic optimization, regular stochastic programming (SP) or simulation technique. Nevertheless, in data‐driven environment, the real passenger demands normally follow complicating probability distribution which cannot be described exactly by the parametric approaches. Hence, we propose a novel data‐driven optimization framework that integrates robust kernel density estimation (RKDE) and the two‐stage SP modeling technique. In particular, the probability distributions of customer demands are derived from historical data by RKDE, and the ETDP is formulated as a two‐stage SP model with the input parameters from RKDE. Meanwhile, a Monte Carlo method called sample average approximation is introduced to reformulate and solve the SP model. Finally, the experimental results show that the proposed approach outperforms the deterministic counterpart with the average demands as the input.

Composite Kernel Association Test (CKAT) for SNP-set joint assessment of genotype and genotype-by-treatment interaction in Pharmacogenetics studies.

It is of substantial interest to discover novel genetic markers that influence drug response in order to develop personalized treatment strategies that maximize therapeutic efficacy and safety. To help enable such discoveries, we focus on testing the association between the cumulative effect of multiple single nucleotide polymorphisms (SNPs) in a particular genomic region and a drug response of interest. However, the currently existing methods are either computational inefficient or not able to control type I error and provide decent power for whole exome or genome analysis in Pharmacogenetics (PGx) studies with small sample sizes. In this article, we propose the Composite Kernel Association Test (CKAT), a flexible and robust kernel machine-based approach to jointly test the genetic main effect and SNP-treatment interaction effect for SNP-sets in Pharmacogenetics (PGx) assessments embedded within randomized clinical trials. An analytic procedure is developed to accurately calculate the P-value so that computationally extensive procedures (e.g. permutation or perturbation) can be avoided. We evaluate CKAT through extensive simulation studies and application to the gene-level association test of the reduction in Clostridium difficile infection recurrence in patients treated with bezlotoxumab. The results demonstrate that the proposed CKAT controls type I error well for PGx studies, is efficient for whole exome/genome association analysis and provides better power performance than existing methods across multiple scenarios. The R package CKAT is publicly available on CRAN https://cran.r-project.org/web/packages/CKAT/. Supplementary data are available at Bioinformatics online.

Point and Interval Solar Power Forecasting Using Hybrid Empirical Wavelet Transform and Robust Wavelet Kernel Ridge Regression

In this paper, a new and efficient hybrid empirical wavelet transform (EWT)-based reduced robust Mexican hat wavelet kernel ridge regression (RMHWK) model is proposed to achieve both point and interval forecasting of solar power in a smart grid scenario. Initially, the actual nonlinear solar power data series was decomposed by the EWT method. A reduced robust kernel ridge regression (RKRR) approach was incorporated that shows a notable decrease in training time without appreciable loss in forecasting accuracy. The reduction in the size of the kernel matrix was achieved by selecting a set of random support vectors from the training data set. For validating the superior performance of the proposed EWT-RMHWK forecasting model, a numerical experimentation implementing a real-time data set of 1 MW solar power plant (Odisha, India) as well as an online historical data set (Florida, USA) was considered and compared with other hybrid models using either empirical mode decomposition- or wavelet decomposition-based RKRR and EWT-ELM, etc. The kernel parameters were optimized with the chaotic water cycle algorithm to boost the performance of the proposed prediction model. Further, the proposed EWT-RKRR method was used to construct prediction interval forecasting with three different confidence levels with 90%, 95%, and 99% for Florida solar power plant using different time horizons of 15 min, 1 h, and 1 day, respectively.

A low rank robust kernel ridge regression classifier for power quality disturbance pattern recognition

This paper presents the development of a new low rank robust kernel ridge regression (KRR) classifier for power quality (PQ) disturbance pattern recognition. It is well known that the kernel methods are used extensively for regression and classification problems using support vector machines (SVM) by mapping the original nonlinear data into a high-dimensional space thereby increasing the generalization performance, and accuracy of classification. On the other hand, the nonlinear kernel ridge regression approach is known for its simple implementation, fast processing speed and accuracy in comparison to the widely used least square support vector machine (LS-SVM). However, for large scale training patterns, the size of kernel matrix becomes large thereby the execution time becomes prohibitive. Besides, the presence of noise and outliers in the data affects the accuracy of the conventional KRR classifier. This paper, therefore, attempts to develop a dimensionally reduced but robust KRR classifier by choosing a random set of support vectors from the training subset to reduce substantially the training time at the cost of a slight loss in accuracy. Further, the KRR algorithm is modified by using a new objective function to minimize the mean and variance of the error to provide robustness and accuracy. For applying this new classifier to power quality disturbance events three relatively new signal processing techniques like the Short-time modified Hilbert Transform (STMHT), Morphological filters, and Fourier kernel S-transform are used to extract the relevant features from the data samples. The simulation results imply that the proposed methods have a higher recognition rate compared with other established techniques such as ELM and Poly SVM while classifying the PQ disturbances. A PC integrated hardware assembly has been used to verify the PQ events classification in real-time.

Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization.

As a nonlinear similarity measure defined in the kernel space, the correntropic loss (C-Loss) can address the stability issues of second-order similarity measures thanks to its ability to extract high-order statistics of data. However, the kernel adaptive filter (KAF) based on the C-Loss uses the stochastic gradient descent (SGD) method to update its weights and, thus, suffers from poor performance and a slow convergence rate. To address these issues, the conjugate gradient (CG)-based correntropy algorithm is developed by solving the combination of half-quadratic (HQ) optimization and weighted least-squares (LS) problems, generating a novel robust kernel correntropy CG (KCCG) algorithm. The proposed KCCG with less computational complexity achieves comparable performance to the kernel recursive maximum correntropy (KRMC) algorithm. To further curb the growth of the network in KCCG, the random Fourier features KCCG (RFFKCCG) algorithm is proposed by transforming the original input data into a fixed-dimensional random Fourier features space (RFFS). Since only one current error information is used in the loss function of RFFKCCG, it can provide a more efficient filter structure than the other KAFs with sparsification. The Monte Carlo simulations conducted in the prediction of synthetic and real-world chaotic time series and the regression for large-scale datasets validate the superiorities of the proposed algorithms in terms of robustness, filtering accuracy, and complexity.

Robust kernel association testing (RobKAT).

Testing the association between single-nucleotide polymorphism (SNP) effects and a response is often carried out through kernel machine methods based on least squares, such as the sequence kernel association test (SKAT). However, these least-squares procedures are designed for a normally distributed conditional response, which may not apply. Other robust procedures such as the quantile regression kernel machine (QRKM) restrict the choice of the loss function and only allow inference on conditional quantiles. We propose a general and robust kernel association test with a flexible choice of the loss function, no distributional assumptions, and has SKAT and QRKM as special cases. We evaluate our proposed robust association test (RobKAT) across various data distributions through a simulation study. When errors are normally distributed, RobKAT controls type I error and shows comparable power with SKAT. In all other distributional settings investigated, our robust test has similar or greater power than SKAT. Finally, we apply our robust testing method to data from the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) clinical trial to detect associations between selected genes including the major histocompatibility complex (MHC) region on chromosome six and neurotropic herpesvirus antibody levels in schizophrenia patients. RobKAT detected significant association with four SNP sets (HST1H2BJ, MHC, POM12L2, and SLC17A1), three of which were undetected by SKAT.

Solar power forecasting using robust kernel extreme learning machine and decomposition methods

This paper proposes empirical mode decomposition (EMD)-based robust kernel extreme learning machine (RKELM) to achieve a precise predicted value of solar power generation in a smart grid environment. The non-stationary historical solar power data is initially decomposed into various intrinsic mode functions (IMFs) using EMD, which are subsequently passed through the proposed robust Morlet wavelet kernel extreme learning machine (RWKELM) for solar power prediction at different time horizons. Further a reduced kernel matrix version of RWKELM is used to decrease the training time significantly without appreciable loss of forecasting accuracy. By implementing the real time data for validation of the proposed method for short term solar power prediction it can be observed that the proposed EMD-based RWKELM outperforms various other methods, in terms of different performance matrices and execution time. The solar power prediction results on experimental data show the lowest error which proves the highest prediction accuracy.

Solar power forecasting using robust kernel extreme learning machine and decomposition methods

Solar power forecasting using robust kernel extreme learning machine and decomposition methods