Search

This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α = 1.007 , implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio's diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure. [ABSTRACT FROM AUTHOR]

The presence of missing components in incomplete instances precludes a kernel-based model from incorporating partially observed components of incomplete instances and computing kernels, including Gaussian kernels that are extensively used in machine learning modeling and applications. Existing methods with Gaussian kernels to handle incomplete data, however, are based on independence among variables. In this study, we propose a new method, the expected Gaussian kernel with correlated variables, that estimates the Gaussian kernel with incomplete data, by considering the correlation among variables. In the proposed method, the squared distance between two instance vectors is modeled with the sum of the correlated squared unit-dimensional distances between the instances, and the Gaussian kernel with missing values is obtained by estimating the expected Gaussian kernel function under the probability distribution for the squared distance between the vectors. The proposed method is evaluated on synthetic data and real-life data from benchmarks and a case from a multi-pattern photolithographic process for wafer fabrication in semiconductor manufacturing. The experimental results show the improvement by the proposed method in the estimation of Gaussian kernels with incomplete data of correlated variables. [ABSTRACT FROM AUTHOR]

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and the Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways of discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region, to aim at suppressing some of the severe artefacts of sampled Gaussian kernels and sampled Gaussian derivatives at very fine scales, or (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data. We study the properties of these three main discretization methods both theoretically and experimentally and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and the sampled Gaussian derivatives as well as the integrated Gaussian kernels and the integrated Gaussian derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in most of the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing. Below a standard deviation of about 0.75, the derivative estimates obtained from convolutions with the sampled Gaussian derivative kernels are, however, not numerically accurate or consistent, while the results obtained from the discrete analogue of the Gaussian kernel, with its associated central difference operators applied to the spatially smoothed image data, are then a much better choice. [ABSTRACT FROM AUTHOR]

Effective drought management requires precise measurement, but this is challenging due to the variety of drought indices and indicators, each with unique methods and specific uses, and limited ground data availability. This study utilizes remote sensing data from 2001 to 2020 to compute drought indices categorized as meteorological, agricultural, and hydrological. A Gaussian kernel convolves these indices into a denoised, multi-band composite image. Further refinement with a Gaussian kernel enhances a single drought index from each category: Reconnaissance Drought Index (RDI), Soil Moisture Agricultural Drought Index (SMADI), and Streamflow Drought Index (SDI). The enhanced index, encompassing all bands, serves as a predictor for classification and regression tree (CART), support vector machine (SVM), and random forest (RF) machine learning models, further improving the three indices. CART demonstrated the highest accuracy and error minimization across all drought categories, with root mean square error (RMSE) and mean absolute error (MAE) values between 0 and 0.4. RF ranked second, while SVM, though less reliable, achieved values below 0.7. The results show persistent drought in the Sahel, North Africa, and southwestern Africa, with meteorological drought affecting 30% of Africa, agricultural drought affecting 22%, and hydrological drought affecting 21%. [ABSTRACT FROM AUTHOR]

This paper investigates the potential of utilising multilevel quasi-interpolation techniques on Chebyshev sparse grids for complex numerical computations. The paper starts by laying down the motivations for choosing Chebyshev sparse grids and quasi-interpolation methods with Gaussian kernels. It delves into the practical aspects of implementing these techniques. Various numerical experiments are performed to evaluate the efficiency and limitations of the multilevel quasi-sparse interpolation methods with dimensions two dimension and three dimension. The work ultimately aims to provide a comprehensive understanding of the computational efficiency and accuracy achievable through this approach, comparing its performance with traditional methods. [ABSTRACT FROM AUTHOR]

Abstract Background Protein-protein interactions (PPIs) hold significant importance in biology, with precise PPI prediction as a pivotal factor in comprehending cellular processes and facilitating drug design. However, experimental determination of PPIs is laborious, time-consuming, and often constrained by technical limitations. Methods We introduce a new node representation method based on initial information fusion, called FFANE, which amalgamates PPI networks and protein sequence data to enhance the precision of PPIs’ prediction. A Gaussian kernel similarity matrix is initially established by leveraging protein structural resemblances. Concurrently, protein sequence similarities are gauged using the Levenshtein distance, enabling the capture of diverse protein attributes. Subsequently, to construct an initial information matrix, these two feature matrices are merged by employing weighted fusion to achieve an organic amalgamation of structural and sequence details. To gain a more profound understanding of the amalgamated features, a Stacked Autoencoder (SAE) is employed for encoding learning, thereby yielding more representative feature representations. Ultimately, classification models are trained to predict PPIs by using the well-learned fusion feature. Results When employing 5-fold cross-validation experiments on SVM, our proposed method achieved average accuracies of 94.28%, 97.69%, and 84.05% in terms of Saccharomyces cerevisiae, Homo sapiens, and Helicobacter pylori datasets, respectively. Conclusion Experimental findings across various authentic datasets validate the efficacy and superiority of this fusion feature representation approach, underscoring its potential value in bioinformatics.

Deep learning-based 3D target detection methods need to solve the problem of insufficient 3D target detection accuracy. In this paper, the KM3D network is selected as the benchmark network after the experimental comparison of current mainstream algorithms, and the IAE-KM3D network algorithm based on the KM3D network is proposed. First, the Resnet V2 network is introduced, and the residual module is redesigned to improve the training capability of the new residual module with higher generalization. IBN NET is then introduced to carefully integrate instance normalization and batch normalization as building blocks to improve the model's detection accuracy in hue- and brightness-changing scenarios without increasing time loss. Then, a parameter-free attention mechanism, Simam, is introduced to improve the detection accuracy of the model. After that, the elliptical Gaussian kernel is introduced to improve the algorithm's ability to detect 3D targets. Finally, a new key point loss function is proposed to improve the algorithm's ability to train. Experiments using the KITTI dataset conclude that the IAE-KM3D network model significantly improves detection accuracy and outperforms the KM3D algorithm regarding detection performance compared to the original KM3D network. The improvements for AP2D, AP3D, and APBEV are 5%, 12.5%, and 8.3%, respectively, and only a tiny amount of time loss and network parameters are added. Compared with other mainstream target detection algorithms, Monn3D, 3DOP, GS3D, and FQNet, the improved IAE-KM3D network in this paper significantly improves AP3D and APBEV, with fewer network parameters and shorter time consumption. [ABSTRACT FROM AUTHOR]

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Chan-Vese (C-V) model for image segmentation and obtain its numerical solution accurately and efficiently. For this purpose, we present a local radial basis function method based on a Gaussian kernel (GA-LRBF) for spatial discretization. Compared to the standard radial basis function method, this approach consumes less CPU time and maintains good stability because it uses only a small subset of points in the whole computational domain. Additionally, since the Gaussian function has the property of dimensional separation, the GA-LRBFmethod is suitable for dealing with isotropic images. Finally, a numerical scheme that couples GA-LRBF with the fourth-order Runge-Kutta method is applied to the C-V model, and a comparison of some numerical results demonstrates that this scheme achieves much more reliable image segmentation. [ABSTRACT FROM AUTHOR]

Over the last decades, learning methods using kernels have become very popular. The main reason is that real data analysis often requires nonlinear methods to detect the dependencies that allow successful predictions of properties of interest. Gaussian kernels have been used in many studies such as learning algorithms and data analysis. Most of these studies have shown that the parameter chosen for a Gaussian kernel could have a huge impact on the desired results. Therefore, it is essential to understand this impact on a theoretical level. The main contribution of this paper is to study the effect of the Gaussian kernel bandwidth parameter on how well an empirical operator defined from data approximates its continuous counterpart. Some results in spectral approximations are provided as well as some examples.

In this paper, we present an algorithm for clustering multidimensional data, which we named TreeKDE. It is based on a tree structure decision associated with the optimization of the one-dimensional kernel density estimator function constructed from the orthogonal projections of the data on the coordinate axes. Among the main features of the proposed algorithm, we highlight the automatic determination of the number of clusters and their insertion in a rectangular region. Comparative numerical experiments are presented to illustrate the performance of the proposed algorithm and the results indicate that the TreeKDE is efficient and competitive when compared to other algorithms from the literature. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field, which can be used as a basis for its improvement, and also for the development of new clustering algorithms based on the association between decision tree and kernel density estimator. [ABSTRACT FROM AUTHOR]

In this paper, we give a new approach to the theory of kernel functions. Our method is based on the structure of Fock spaces. As its applications, two non-Euclidean examples of strictly positive kernel functions are given. Moreover, we give a new proof of the universal approximation theorem for Gaussian type kernels. [ABSTRACT FROM AUTHOR]

This paper investigates the potential of utilising multilevel quasi-interpolation techniques on Chebyshev sparse grids for complex numerical computations. The paper starts by laying down the motivations for choosing Chebyshev sparse grids and quasi-interpolation methods with Gaussian kernels. It delves into the practical aspects of implementing these techniques. Various numerical experiments are performed to evaluate the efficiency and limitations of the multilevel quasi-sparse interpolation methods with dimensions two dimension and three dimension. The work ultimately aims to provide a comprehensive understanding of the computational efficiency and accuracy achievable through this approach, comparing its performance with traditional methods.

For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller than the size of the surrounding tissues. Here, we consider the scenario that the cell or the vesicle releases the diffusive compounds to the immediate environment, which is modelled by the diffusion equation. Typically, one separates the intracellular and extracellular environment and uses homogeneous Neumann boundary condition for the cell boundary (so-called spatial exclusion model), while the point source model neglects the intracellular environment. We show that extra conditions are needed such that the solutions to the two models are consistent. We prove a necessary and sufficient condition for the consistency. Suggested by the numerical results, we conclude that an initial condition in the form of Gaussian kernel in the point source model compensates for a time-delay discrepancy between the solutions to the two models in the numerical solutions. Various approaches determining optimal amplitude and variance of the Gaussian kernel have been discussed. [ABSTRACT FROM AUTHOR]

Abstract Background The limited knowledge of miRNA–lncRNA interactions is considered as an obstruction of revealing the regulatory mechanism. Accumulating evidence on Human diseases indicates that the modulation of gene expression has a great relationship with the interactions between miRNAs and lncRNAs. However, such interaction validation via crosslinking-immunoprecipitation and high-throughput sequencing (CLIP-seq) experiments that inevitably costs too much money and time but with unsatisfactory results. Therefore, more and more computational prediction tools have been developed to offer many reliable candidates for a better design of further bio-experiments. Methods In this work, we proposed a novel link prediction model based on Gaussian kernel-based method and linear optimization algorithm for inferring miRNA–lncRNA interactions (GKLOMLI). Given an observed miRNA–lncRNA interaction network, the Gaussian kernel-based method was employed to output two similarity matrixes of miRNAs and lncRNAs. Based on the integrated matrix combined with similarity matrixes and the observed interaction network, a linear optimization-based link prediction model was trained for inferring miRNA–lncRNA interactions. Results To evaluate the performance of our proposed method, k-fold cross-validation (CV) and leave-one-out CV were implemented, in which each CV experiment was carried out 100 times on a training set generated randomly. The high area under the curves (AUCs) at 0.8623 ± 0.0027 (2-fold CV), 0.9053 ± 0.0017 (5-fold CV), 0.9151 ± 0.0013 (10-fold CV), and 0.9236 (LOO-CV), illustrated the precision and reliability of our proposed method. Conclusion GKLOMLI with high performance is anticipated to be used to reveal underlying interactions between miRNA and their target lncRNAs, and deciphers the potential mechanisms of the complex diseases.

Deep learning-based 3D target detection methods need to solve the problem of insufficient 3D target detection accuracy. In this paper, the KM3D network is selected as the benchmark network after the experimental comparison of current mainstream algorithms, and the IAE-KM3D network algorithm based on the KM3D network is proposed. First, the Resnet V2 network is introduced, and the residual module is redesigned to improve the training capability of the new residual module with higher generalization. IBN NET is then introduced to carefully integrate instance normalization and batch normalization as building blocks to improve the model’s detection accuracy in hue- and brightness-changing scenarios without increasing time loss. Then, a parameter-free attention mechanism, Simam, is introduced to improve the detection accuracy of the model. After that, the elliptical Gaussian kernel is introduced to improve the algorithm’s ability to detect 3D targets. Finally, a new key point loss function is proposed to improve the algorithm’s ability to train. Experiments using the KITTI dataset conclude that the IAE-KM3D network model significantly improves detection accuracy and outperforms the KM3D algorithm regarding detection performance compared to the original KM3D network. The improvements for AP2D, AP3D, and APBEV are 5%, 12.5%, and 8.3%, respectively, and only a tiny amount of time loss and network parameters are added. Compared with other mainstream target detection algorithms, Monn3D, 3DOP, GS3D, and FQNet, the improved IAE-KM3D network in this paper significantly improves AP3D and APBEV, with fewer network parameters and shorter time consumption.

In this work, a novel weighted kernel least mean square (WKLMS) algorithm is proposed by introducing a weighted Gaussian kernel. The learning behavior of the WKLMS algorithm is studied. Mean square error (MSE) analysis shows that the WKLMS algorithm outperforms both the least mean square (LMS) and KLMS algorithms in terms of transient state as well as steady-state responses. We study the effect of the weighted Gaussian kernel on the associated kernel matrix, its eigenvalue spread and distribution, and show how these parameters affect the convergence behavior of the algorithm. Both of the transient and steady-state mean-square-error (MSE) behaviors of the WKLMS algorithm are studied, and a stability bound is derived. For a non-stationary environment, tracking analysis for a correlated random walk channel is presented. We also prove that the steady-state excess MSE (EMSE) of the WKLMS is Schur convex function of the weight elements in its kernel weight matrix and hence it follows the majorization of the kernel weight elements. This helps to decide which kernel weight matrix can provide better MSE performance. Simulations results are provided to contrast the performance of the proposed WKLMS with those of its counterparts KLMS and LMS algorithms. The derived analytical results of the proposed WKLMS algorithm are also validated via simulations for various step-size values. [ABSTRACT FROM AUTHOR]

Knowledge-based systems developed based on Dempster–Shafer theory and prospect theory enhances decision-making under uncertainty. But at times, the traditional two-way decision approach may not be able to suggest a suitable decision confidently. This work proposes a three-way decision support system which divides the alternatives into three disjoint sets. Nonparametric Gaussian kernel and mid-range values are used to compute basic probabilities and reference points, respectively. The difference between basic probabilities and reference points is considered for assigning gain–loss values based on the value function from prospect theory. Ten publicly available benchmark data sets are considered, and the effectiveness of the proposed system is affirmed by comparing its performance with traditional machine learning models and other relevant decision-making systems in the literature. A case study related to evaluation of candidates is included, and it is also compared with other reference point estimation methods. From the results, it can be inferred that considering mid-range values as reference generates a preference order that is intuitive and compliable. [ABSTRACT FROM AUTHOR]

In this paper, we propose a threshold dynamics method for the Willmore flow with a new kernel constructed based on the combination of a Gaussian kernel and a Cosine function. We show the consistency of the method by asymptotic analysis and construct a Lyapunov functional to show the unconditional stability of the proposed method. Compare to previous work, no artificial parameters are required for the construction of the kernel. Numerical experiments including area preservation or perimeter preservation are performed to show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Spatial smoothing is a preprocessing step applied to neuroimaging data to enhance data quality by reducing noise and artifacts. However, selecting an appropriate smoothing kernel size can be challenging as it can lead to undesired alterations in final images and functional connectivity networks. However, there is no sufficient information about the effects of the Gaussian kernel size on group-level results for different cases yet. This study investigates the influence of kernel size on functional connectivity networks and network parameters in whole-brain rs-fMRI and tb-fMRI analyses of healthy adults. The analysis includes {0, 2, 4, 6, 8, 10} mm kernels, commonly used in practical analyses, covering all major brain networks. Graph theoretical measures such as betweenness centrality, global/local efficiency, clustering coefficient, and average path length are examined for each kernel. Additionally, principal component analysis (PCA) and independent component analysis (ICA) parameters, namely kurtosis and skewness, are evaluated for the functional images. The findings demonstrate that kernel size directly affects node connections, resulting in modifications to functional network structures and PCA/ICA parameters. However, network metrics exhibit greater resilience to these changes. [ABSTRACT FROM AUTHOR]

The number of drug abuse cases in Indonesia from 2015-2020 tends to fluctuate. Factors influencing drug abuse cases in each region are thought to vary according to geographical location. This geographic effect is known as spatial heterogeneity. Spatial heterogeneity was analyzed usingGeographically Weighted Regression(GWR). This study aims to model the factors that influence drug abuse in every province in Indonesia, namely Economic Situation (X1), Association/Environment (X2), Convenience (X3) and Lack of Supervision (X4) using a Gaussian kernel. The results showed that the GWR with the Gaussian kernel is better at estimating the model because it has a higher value, namely R^2 with 90.94% and the AIC value equals 598.798979. Factors that significantly affect the number of cases of drug abuse in Indonesia are Economic Conditions, Association/Environment, Convenience and Lack of Supervision.

To develop a system for specific purpose, it needs to estimate its parameters (parameterization). It can be used in different fields like engineering, industry etc. In this work, authors used adaptive algorithm to model a system that is applicable in industry for control. This adaptive model is non-linear where its estimation is based on kernel based Least-mean square (LMS) algorithm. The kernel used as Polynomial and Gaussian. As the system is nonlinear polynomial kernel-based algorithm fails to prove its efficacy, though it is of low complexity approach. Gaussian kernel-based application for nonlinear system control performance better as compared to polynomial kernel. Further its complexity is reduced and used for faster performance. The result shows its performance in form of MSE, MAE, RMSE for identification and control that is very useful in industrial application.

We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the projections of the response vector Y on leading principle components of a kernel matrix fixed and permute Y's projections on the remaining principle components. The proposed test allows for different choices of kernels, corresponding to different classes of functions under the null hypothesis. First, using linear or polynomial kernels, our partial permutation tests are exactly valid in finite samples for linear or polynomial regression models with Gaussian noise; similar results straightforwardly extend to kernels with finite feature spaces. Second, by allowing the kernel feature space to diverge with the sample size, the test can be large-sample valid for a wider class of functions. Third, for general kernels with possibly infinite-dimensional feature space, the partial permutation test is exactly valid when the covariates are exactly balanced across all groups, or asymptotically valid when the underlying function follows certain regularized Gaussian processes. We further suggest test statistics using likelihood ratio between two (nested) Gaussian process regression models, and propose computationally efficient algorithms utilizing the EM algorithm and Newton's method, where the latter also involves Fisher scoring and quadratic programming and is particularly useful when EM suffers from slow convergence. Extensions to correlated and non-Gaussian noises have also been investigated theoretically or numerically. Furthermore, the test can be extended to use multiple kernels together and can thus enjoy properties from each kernel. Both simulation study and application illustrate the properties of the proposed test. [ABSTRACT FROM AUTHOR]

We derive a generic system that constructs an optimization model for an emergency stop scenario on the highway, based on map data from high definition maps that are used in Advanced Driver Assistance Systems (ADAS) and in Highly Automated Driving (HAD). New additional situative and scenario-based information is computed by applying a global maximization approach to the model. For this purpose, we develop two new rigorous and deterministic branch-and-bound algorithms that both determine the certified global optimal value up to a predefined tolerance. The underlying interval optimization algorithm, which uses first-order techniques, is enhanced by one of two second-order methods that are applied for specifically selected intervals. We investigate two approaches that either compute a concave overestimator for the objective function or approximate the function with a quadratic polynomial using Taylor expansion. We show the limits of interval arithmetic in our problem, especially for the interval versions of the derivatives, and present a local linearization of the curve data that improves the results significantly. The presented novel method for deriving secondary information is compared to state of the art methods on two exemplary and for the automotive context representative scenarios to show the advantages of our approach. [ABSTRACT FROM AUTHOR]

Background: The limited knowledge of miRNA–lncRNA interactions is considered as an obstruction of revealing the regulatory mechanism. Accumulating evidence on Human diseases indicates that the modulation of gene expression has a great relationship with the interactions between miRNAs and lncRNAs. However, such interaction validation via crosslinking-immunoprecipitation and high-throughput sequencing (CLIP-seq) experiments that inevitably costs too much money and time but with unsatisfactory results. Therefore, more and more computational prediction tools have been developed to offer many reliable candidates for a better design of further bio-experiments. Methods: In this work, we proposed a novel link prediction model based on Gaussian kernel-based method and linear optimization algorithm for inferring miRNA–lncRNA interactions (GKLOMLI). Given an observed miRNA–lncRNA interaction network, the Gaussian kernel-based method was employed to output two similarity matrixes of miRNAs and lncRNAs. Based on the integrated matrix combined with similarity matrixes and the observed interaction network, a linear optimization-based link prediction model was trained for inferring miRNA–lncRNA interactions. Results: To evaluate the performance of our proposed method, k-fold cross-validation (CV) and leave-one-out CV were implemented, in which each CV experiment was carried out 100 times on a training set generated randomly. The high area under the curves (AUCs) at 0.8623 ± 0.0027 (2-fold CV), 0.9053 ± 0.0017 (5-fold CV), 0.9151 ± 0.0013 (10-fold CV), and 0.9236 (LOO-CV), illustrated the precision and reliability of our proposed method. Conclusion: GKLOMLI with high performance is anticipated to be used to reveal underlying interactions between miRNA and their target lncRNAs, and deciphers the potential mechanisms of the complex diseases. [ABSTRACT FROM AUTHOR]

In this article, a stochastic gradient algorithm based on the minimum Shannon entropy is proposed to identify a type of Hammerstein system with random noise. Firstly, the probability density function is estimated by a parzen window based on the Gaussian kernel. Then, the traditional stochastic gradient algorithm is adopted to estimate the parameters. However, the traditional stochastic gradient algorithm converges quite slowly. To fasten the algorithm, a multierror method is integrated into the algorithm. In this multierror gradient algorithm, the scalar error is replaced by a vector error. This vector error can accelerate the algorithm greatly and give a more accurate estimate by using the same data set. Finally, the proposed algorithm is validated by a numerical example and an industrial process. The estimation results indicate that the proposed algorithm can obtain more accurate estimates than the traditional gradient algorithm and has a faster convergence speed. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Data Acquisition & Processing / Shu Ju Cai Ji Yu Chu Li is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Currently, neighborhood linear discriminant analysis (nLDA) exploits reverse nearest neighbors (RNN) to avoid the assumption of linear discriminant analysis (LDA) that all samples from the same class should be independently and identically distributed (i.i.d.). nLDA performs well when a dataset contains multimodal classes. However, in complex pattern recognition tasks, such as visual classification, the complex appearance variations caused by deformation, illumination and visual angle often generate non-linearity. Furthermore, it is not easy to separate the multimodal classes in lower-dimensional feature space. One solution to these problems is to map the feature to a higher-dimensional feature space for discriminant learning. Hence, in this paper, we employ kernel functions to map the original data to a higher-dimensional feature space, where the nonlinear multimodal classes can be better classified. We give the details of the deduction of the proposed kernel reverse neighborhood discriminant analysis (KRNDA) with the kernel tricks. The proposed KRNDA outperforms the original nLDA on most datasets of the UCI benchmark database. In high-dimensional visual recognition tasks of handwritten digit recognition, object categorization and face recognition, our KRNDA achieves the best recognition results compared to several sophisticated LDA-based discriminators. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Engineering & Applications is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper three prime numbers are presented as high potentials to be Mersenne numbers and their application in computational primality testing is suggested. These numbers are constructed from a regression algorithm based on Support vector machines (SVM) and using a Gaussian Kernel. Data training is carried out using the Phyton programming language, In the study we address the current data of Mersenne primes and work with the Ova-angular classification group for Mersenne primes 31. [ABSTRACT FROM AUTHOR]

Data clustering is an essential tool for entering the data world. Quantum clustering (QC) is a meta-heuristic method derived from the Schrödinger equation and incorporates some concepts of quantum mechanics. QC shows a very high ability to adapt to data distribution and finding data structure. The data are clustered by the extremes of the potential function obtained from the Schrödinger equation. QC has a length parameter that plays an important task in determining the number and location of extremes of the potential function. The length parameter is the width of the Gaussian kernel that is included as a wave function in the Schrödinger equation. In this paper, we use a simple method to estimate the width of the Gaussian kernel based on an adaptive scaling technique. In adaptive scaling quantum clustering (ASQC), global hyper-parameter of QC is replaced by a local hyper-parameter. By this technique, the effects of local density are entered in QC, the necessary parameters for this model are calculated by algorithm and the clustering results are improved. [ABSTRACT FROM AUTHOR]

Random Fourier features are a popular technique used to improve nonlinear kernel methods in large-scale problems. Recent studies have shown that replacing random Gaussian matrices of random feature maps with appropriately scaled random orthogonal matrices, such as SORF, can significantly improve kernel approximation performance. However, the SORF method theoretically requires zero-padding for datasets whose input feature dimension does not meet d = 2 p for some p ∈ N + , resulting in increased memory and computation time. To address this limitation, we propose a new structured orthogonal random features method based on discrete cosine transform (SORF-DCT) to approximate Gaussian kernel functions. The SORF-DCT method does not require the input feature dimension to be d = 2 p . The key to SORF-DCT is that we combine the DCT matrix with diagonal "sign-flipping" matrices and scale them appropriately using a diagonal matrix whose diagonal elements follow the chi distribution, resulting in a structured orthogonal matrix whose elements follow the standard Gaussian distribution instead of a random Gaussian matrix. SORF-DCT generates D -dimensional structured orthogonal random features in O (D log d) time and O (D) memory by employing fast discrete cosine transform, where d and D represent the input feature dimension and expansion dimension, respectively. We prove that SORF-DCT is an unbiased estimator of the Gaussian kernel function and analyze the concentration error bounds. Experimental results on eleven benchmark datasets show that SORF-DCT achieves lower kernel approximation errors, requires less time, and has comparable nonlinear learning capabilities. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel semi-analytical method to model complicated material interfaces by using a Gaussian kernel function and the resulting error function (erf) available in the symbolic toolbox of MATLAB. The proposed method provides an analytical expression for the smoothened material properties via a diffused representation of material interfaces that eliminates the requirement to track material interfaces explicitly while implementing the finite element method. In this article, we have demonstrated the proposed diffused representation approach for the homogenization of composites with periodic microstructures. We have studied the influence of varying shapes and sizes of inclusion on the overall effective material properties and the elastic response of the homogenized composites. However, the method is very generic and can be applied to obtain an analytical expression for smoothened material properties for any complicated material interface that may be useful to design high-performance topologically interlocked composites. [ABSTRACT FROM AUTHOR]

Genomic prediction is revolutionizing plant breeding since candidate genotypes can be selected without the need to measure their trait in the field. When a reference population contains both phenotypic and genotypic information, it is trained by a statistical machine learning method that is subsequently used for making predictions of breeding or phenotypic values of candidate genotypes that were only genotyped. Nevertheless, the successful implementation of the genomic selection (GS) methodology depends on many factors. One key factor is the type of statistical machine learning method used since some are unable to capture nonlinear patterns available in the data. While kernel methods are powerful statistical machine learning algorithms that capture complex nonlinear patterns in the data, their successful implementation strongly depends on the careful tuning process of the involved hyperparameters. As such, in this paper we compare three methods of tuning (manual tuning, grid search, and Bayesian optimization) for the Gaussian kernel under a Bayesian best linear unbiased predictor model. We used six real datasets of wheat (Triticum aestivum L.) to compare the three strategies of tuning. We found that if we want to obtain the major benefits of using Gaussian kernels, it is very important to perform a careful tuning process. The best prediction performance was observed when the tuning process was performed with grid search and Bayesian optimization. However, we did not observe relevant differences between the grid search and Bayesian optimization approach. The observed gains in terms of prediction performance were between 2.1% and 27.8% across the six datasets under study. [ABSTRACT FROM AUTHOR]

We study the spectral convergence of graph Laplacians to the Laplace-Beltrami operator when the kernelized graph affinity matrix is constructed from N random samples on a d -dimensional manifold in an ambient Euclidean space. By analyzing Dirichlet form convergence and constructing candidate approximate eigenfunctions via convolution with manifold heat kernel, we prove eigen-convergence with rates as N increases. The best eigenvalue convergence rate is N − 1 / (d / 2 + 2) (when the kernel bandwidth parameter ϵ ∼ (log ⁡ N / N) 1 / (d / 2 + 2)) and the best eigenvector 2-norm convergence rate is N − 1 / (d / 2 + 3) (when ϵ ∼ (log ⁡ N / N) 1 / (d / 2 + 3)). These rates hold up to a log ⁡ N -factor for finitely many low-lying eigenvalues of both un-normalized and normalized graph Laplacians. When data density is non-uniform, we prove the same rates for the density-corrected graph Laplacian, and we also establish new operator point-wise convergence rate and Dirichlet form convergence rate as intermediate results. Numerical results are provided to support the theory. [ABSTRACT FROM AUTHOR]

Robust design optimization (RDO) is one of the most popular methodologies in the presence of uncertainties, which aims to provide an insensitive design configuration. However, the assessment of the robustness index is computationally intensive for practical engineering. Surrogate assisted optimization is an effective way to reduce the computational expense. Various surrogate models have been used in RDO, such as support vector regression, Kriging, artificial neural network, radial basis function and so on. Recently, a new surrogate model named PC-GK-SBL is proposed, combining the polynomial chaos expansion (PCE) and Gaussian kernel (GK) in the sparse Bayesian learning (SBL) framework. In this paper, the PC-GK-SBL surrogate model is integrated into RDO, and the analytical formulae for the robustness index and its sensitivity are derived, which improves computational efficiency significantly. Furthermore, an adaptive active learning function, named robust local geometrical exploration (RLGE), is also proposed to select the new sample points for updating the surrogate model, in which the sigmoid function is combined with distance based geometrical exploration strategy to improve the accuracy of the RDO solution significantly. In RLGE, the sigmoid function is utilized to filter out the design spaces that have little influence on the robustness index, and the geometrical exploration is employed to avoid crowding of the added samples for the surrogate model. The RLGE active learning function is evaluated by a metaheuristic algorithm, the comprehensive learning Harris hawks-equilibrium optimization. Finally, the accuracy and efficiency of the proposed method were demonstrated through four numerical examples and one engineering example. [ABSTRACT FROM AUTHOR]