Comparison of Uniform and Kernel Gaussian Weight Matrix in Generalized Spatial Panel Data Model

Panel data combine cross-section data and time series data. If the cross-section is locations, there is a need to check the correlation among locations. ρ and λ are parameters in generalized spatial model to cover effect of correlation between locations. Value of ρ or λ will influence the goodness of fit model, so it is important to make parameter estimation. The effect of another location is covered by making contiguity matrix until it gets spatial weighted matrix (W). There are some types of W—uniform W, binary W, kernel Gaussian W and some W from real case of economics condition or transportation condition from locations. This study is aimed to compare uniform W and kernel Gaussian W in spatial panel data model using RMSE value. The result of analysis showed that uniform weight had RMSE value less than kernel Gaussian model. Uniform W had stabil value for all the combinations.

Gaussian Kernel Based SVR Model for Short-Term Photovoltaic MPP Power Prediction

Predicting the power obtained at the output of the photovoltaic(PV)system is fundamental for the optimum use of the PV system.However,it varies at different times of the day depending on intermittent and nonlinear environmen-tal conditions including solar irradiation,temperature and the wind speed,Short-term power prediction is vital in PV systems to reconcile generation and demand in terms of the cost and capacity of the reserve.In this study,a Gaussian kernel based Support Vector Regression(SVR)prediction model using multiple input variables is proposed for estimating the maximum power obtained from using per-turb observation method in the different irradiation and the different temperatures for a short-term in the DC-DC boost converter at the PV system.The performance of the kernel-based prediction model depends on the availability of a suitable ker-nel function that matches the learning objective,since an unsuitable kernel func-tion or hyper parameter tuning results in significantly poor performance.In this study for thefirst time in the literature both maximum power is obtained at max-imum power point and short-term maximum power estimation is made.While evaluating the performance of the suggested model,the PV power data simulated at variable irradiations and variable temperatures for one day in the PV system simulated in MATLAB were used.The maximum power obtained from the simu-lated system at maximum irradiance was 852.6 W.The accuracy and the perfor-mance evaluation of suggested forecasting model were identified utilizing the computing error statistics such as root mean square error(RMSE)and mean square error(MSE)values.MSE and RMSE rates which obtained were 4.5566*10-04 and 0.0213 using ANN model.MSE and RMSE rates which obtained were 13.0000*10-04 and 0.0362 using SWD-FFNN model.Using SVR model,1.1548*10-05 MSE and 0.0034 RMSE rates were obtained.In the short-term maximum power prediction,SVR gave higher prediction performance according to ANN and SWD-FFNN.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

ON USING NON-LINEAR CANONICAL CORRELATION ANALYSIS FOR VOICE CONVERSION BASED ON GAUSSIAN MIXTURE MODEL

Voice conversion algorithm aims to provide high level of similarity to the target voice with an acceptable level of quality.The main object of this paper was to build a nonlinear relationship between the parameters for the acoustical features of source and target speaker using Non-Linear Canonical Correlation Analysis(NLCCA) based on jointed Gaussian mixture model.Speaker indi-viduality transformation was achieved mainly by altering vocal tract characteristics represented by Line Spectral Frequencies(LSF).To obtain the transformed speech which sounded more like the target voices,prosody modification is involved through residual prediction.Both objective and subjective evaluations were conducted.The experimental results demonstrated that our proposed algorithm was effective and outperformed the conventional conversion method utilized by the Minimum Mean Square Error(MMSE) estimation.

Multi-output Gaussian Process Regression Model with Combined Kernel Function for Polyester Esterification Processes

In polyester fiber industrial processes,the prediction of key performance indicators is vital for product quality.The esterification process is an indispensable step in the polyester polymerization process.It has the characteristics of strong coupling,nonlinearity and complex mechanism.To solve these problems,we put forward a multi-output Gaussian process regression(MGPR)model based on the combined kernel function for the polyester esterification process.Since the seasonal and trend decomposition using loess(STL)can extract the periodic and trend characteristics of time series,a combined kernel function based on the STL and the kernel function analysis is constructed for the MGPR.The effectiveness of the proposed model is verified by the actual polyester esterification process data collected from fiber production.

复Gaussian小波核函数及多参数同步优化策略

对复Gauss-ian小波满足M ercy条件及其在H ilbert空间具有再生性的命题作了证明.用复Gauss-ian小波构建出一种核函数,与主成分分析方法相结合,对非线性非平稳信号进行参数辨识和预测.针对多参数模型优化时间过长,不利于工程应用的问题,提出了一种多参数同步优化策略.仿真实验验证了该方法的可行性和有效性,表明该方法具有较好的实用价值.

利用Gaussian核对多元函数的近似逼近及其误差估计

V.Maz’ya首次提出了近似逼近法,其主要是研究定义在全空间上的光滑函数的逼近情况,但它不能有效的处理积分和拟微分算子的高阶求积公式问题及利用更有效的数值和半数值方法解决数学物理的边界等问题.F.M櫣ller和W.Varnhorn给出了一维紧区间上函数的近似逼近方法,而且还可以控制近似逼近的截断误差.根据上述思想,采用近似逼近法,利用Gaussian核对二维紧空间上光滑函数进行逼近,并考察由这种近似逼近法所产生的误差情况.

Gaussian小波SVM及其混沌时间序列预测

为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型。证明了偶数阶Gaussian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM。对混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量。用Gaussian小波SVM与常用的径向基SVM及Morlet小波SVM进行对比实验,通过对Chens混沌时间序列和负荷混沌时间序列的预测,结果表明,Gaussian小波SVM的效果比其他两种SVM更好。

Gaussian核SVM在抗噪语音识别中的应用

为提高机器学习的推广能力,解决语音识别系统在噪声环境中识别率变差等问题,采用改进的MFCC语音特征参数,用Gaussian核支持向量机(SVM)作为语音识别网络,对SVM多类分类问题采用"一对一"分类算法,实现了一个汉语孤立词非特定人中等词汇量的抗噪语音识别系统。通过实验,分析了Gaussian核参数和误差惩罚参数C对SVM推广能力的影响。实验结果表明,当工作在不同信噪比情况下,使用最优参数的Gaussion核SVM的识别率比使用RBF神经网络有较大的提高,训练时间能大为缩减,鲁棒性也较好。

基于KPCA-GaussianNB的电子商务信用风险分类

用核主成分分析(KPCA)和高斯朴素贝叶斯(GaussianNB)构建电子商务信用风险分类模型(KPCAGaussianNB)。首先,通过KPCA方法将电子商务信用风险涉及的指标进行主要特征提取;其次,应用GaussianNB方法构造电子商务信用风险分类模型;最后,使用18家电子商务企业的真实数据进行实证检验,并依据检验结果提出应对风险的措施。验证结果表明:通过对比GaussianNB、PCA-GaussianNB和KPCA-GaussianNB的平均准确率,KPCA-GaussianNB的平均准确率最高。

Soft sensor modeling based on Gaussian processes

In order to meet the demand of online optimal running, a novel soft sensor modeling approach based on Gaussian processes was proposed. The approach is moderately simple to implement and use without loss of performance. It is trained by optimizing the hyperparameters using the scaled conjugate gradient algorithm with the squared exponential covariance function employed. Experimental simulations show that the soft sensor modeling approach has the advantage via a real-world example in a refinery. Meanwhile, the method opens new possibilities for application of kernel methods to potential fields.

A Gaussian process regression-based sea surface temperature interpolation algorithm

The resolution of ocean reanalysis datasets is generally low because of the limited resolution of their associated numerical models.Low-resolution ocean reanalysis datasets are therefore usually interpolated to provide an initial or boundary field for higher-resolution regional ocean models.However,traditional interpolation methods(nearest neighbor interpolation,bilinear interpolation,and bicubic interpolation)lack physical constraints and can generate significant errors at land-sea boundaries and around islands.In this paper,a machine learning method is used to design an interpolation algorithm based on Gaussian process regression.The method uses a multiscale kernel function to process two-dimensional space meteorological ocean processes and introduces multiscale physical feature information(sea surface wind stress,sea surface heat flux,and ocean current velocity).This greatly improves the spatial resolution of ocean features and the interpolation accuracy.The eff ectiveness of the algorithm was validated through interpolation experiments relating to sea surface temperature(SST).The root mean square error(RMSE)of the interpolation algorithm was 38.9%,43.7%,and 62.4%lower than that of bilinear interpolation,bicubic interpolation,and nearest neighbor interpolation,respectively.The interpolation accuracy was also significantly better in off shore area and around islands.The algorithm has an acceptable runtime cost and good temporal and spatial generalizability.

A Kernel-Based Nonlinear Representor with Application to Eigenface Classification

This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.

Gaussian核与具有共同光滑性的Sobolev类的学习误差

逼近误差和回归函数的正规性有关。文章研究了Gaussian核和Sobolev共同光滑回归函数的逼近误差,并得到其对数收敛阶。这个结果推广了周定轩有关Sobolev光滑回归函数的逼近误差研究。

Determination of influential parameters for prediction of total sediment loads in mountain rivers using kernel-based approaches

It is important to have a reasonable estimation of sediment transport rate with respect to its significant role in the planning and management of water resources projects. The complicate nature of sediment transport in gravel-bed rivers causes inaccuracies of empirical formulas in the prediction of this phenomenon. Artificial intelligences as alternative approaches can provide solutions to such complex problems. The present study aimed at investigating the capability of kernel-based approaches in predicting total sediment loads and identification of influential parameters of total sediment transport. For this purpose, Gaussian process regression(GPR), Support vector machine(SVM) and kernel extreme learning machine(KELM) are applied to enhance the prediction level of total sediment loads in 19 mountain gravel-bed streams and rivers located in the United States. Several parameters based on two scenarios are investigated and consecutive predicted results are compared with some well-known formulas. Scenario 1 considers only hydraulic characteristics and on the other side, the second scenario was formed using hydraulic and sediment properties. The obtained results reveal that using the parameters of hydraulic conditions asinputs gives a good estimation of total sediment loads. Furthermore, it was revealed that KELM method with input parameters of Froude number(Fr), ratio of average velocity(V) to shear velocity(U*) and shields number(θ) yields a correlation coefficient(R) of 0.951, a Nash-Sutcliffe efficiency(NSE) of 0.903 and root mean squared error(RMSE) of 0.021 and indicates superior results compared with other methods. Performing sensitivity analysis showed that the ratio of average velocity to shear flow velocity and the Froude number are the most effective parameters in predicting total sediment loads of gravel-bed rivers.

Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey

Data-driven paradigms are well-known and salient demands of future wireless communication. Empowered by big data and machine learning techniques,next-generation data-driven communication systems will be intelligent with unique characteristics of expressiveness, scalability, interpretability, and uncertainty awareness, which can confidently involve diversified latent demands and personalized services in the foreseeable future. In this paper, we review a promising family of nonparametric Bayesian machine learning models,i.e., Gaussian processes(GPs), and their applications in wireless communication. Since GP models demonstrate outstanding expressive and interpretable learning ability with uncertainty, they are particularly suitable for wireless communication. Moreover, they provide a natural framework for collaborating data and empirical models(DEM). Specifically, we first envision three-level motivations of data-driven wireless communication using GP models. Then, we present the background of the GPs in terms of covariance structure and model inference. The expressiveness of the GP model using various interpretable kernels, including stationary, non-stationary, deep and multi-task kernels,is showcased. Furthermore, we review the distributed GP models with promising scalability, which is suitable for applications in wireless networks with a large number of distributed edge devices. Finally, we list representative solutions and promising techniques that adopt GP models in various wireless communication applications.

Gaussian process hydrodynamics

We present a Gaussian process(GP)approach,called Gaussian process hydrodynamics(GPH)for approximating the solution to the Euler and Navier-Stokes(NS)equations.Similar to smoothed particle hydrodynamics(SPH),GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow.However,these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow.Closure is achieved by placing a divergence-free GP priorξon the velocity field and conditioning it on the vorticity at the particle locations.Known physics(e.g.,the Richardson cascade and velocityincrement power laws)is incorporated into the GP prior by using physics-informed additive kernels.This is equivalent to expressingξas a sum of independent GPsξl,which we call modes,acting at different scales(each modeξlself-activates to represent the formation of eddies at the corresponding scales).This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes,and enables us to analyze coarse-grain turbulence statistically rather than deterministically.Because GPH is formulated by using the vorticity equations,it does not require solving a pressure equation.By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel,GPH requires significantly fewer particles than SPH.Because GPH has a natural probabilistic interpretation,the numerical results come with uncertainty estimates,enabling their incorporation into an uncertainty quantification(UQ)pipeline and adding/removing particles(quanta of information)in an adapted manner.The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss.Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability.Because the proposed approach uses a Bayesian interpretation,it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

利用SE-GPR模型对甲醇/柴油混合燃料柴油机性能的预测

为了对柴油机的经济性和排放参数进行高效、准确的预测,根据4190型船用柴油机实验数据与边界参数,建立AVL-BOOST甲醇/柴油混合燃料柴油机仿真模型;利用模型进行仿真实验,并建立甲醇掺混比、废气再循环(exhaust gas recirculation,EGR)率、喷油提前角和进气压力4个控制参数对有效油耗率和NO x排放预测数据集;利用该数据集对5种不同核函数的高斯过程回归(Gaussian process regression,GPR)模型进行训练;最后将最优的平方指数高斯过程回归(squared exponential-Gaussian process regression,SE-GPR)模型、AVL-BOOST仿真数据和柴油机实验数据进行对比。结果表明:在数据量为180组时,SE-GPR模型对有效油耗率和NO x排放均取得拟合关联度99%以上,均方根误差(root mean square error,RMSE)分别为1.859,0.3445,平均绝对误差(mean absolute error,MAE)分别为0.954,0.2489;并且,相较于AVL-BOOST仿真实验,SE-GPR模型对实验数据具有更好的拟合性。

不平衡数据集的DC-SMOTE过采样方法

针对不平衡数据集在分类任务中表现不佳的问题,提出基于局部密度与集中度的过采样算法。针对数据集中所有的少数类样本点,分别利用高斯核函数与局部引力来计算局部密度与集中度;对于局部密度较小的部分有针对性地合成第一类新样本,解决类内不平衡问题。根据集中度的不同,区分出少数类样本的边界,有针对性地合成第二类新样本,达到强化边界的作用;同时,通过自适应生成新样本,有效解决大部分过采样算法没有明确过采样量或者盲目追求样本平衡度相等的问题。最后,在公开的12个不平衡数据集上进行了实验,实验结果表明,本算法在低不平衡数据集与高不平衡数据集上的应用均拥有良好的表现。

基于神经核网络高斯过程回归的甲板运动预测

甲板运动预测与补偿是舰载机自动着舰的关键技术之一。传统甲板运动预测方法依赖于运动建模的准确性和参数调整,面临复杂海况、不同舰型、航态变化时具有适应性差、预测时长短、结果可靠性低等问题。提出一种基于神经核网络高斯过程回归(NKN-GPR)的甲板运动预测模型,使用神经核网络(NKN)实现高斯过程回归(GPR)模型自动复合核构造,有效改善基于规则库自动核搜索(ACKS)算法依赖人工先验知识的不足。以正弦波组合模型和功率谱模型构造仿真数据,对NKN-GPR模型和基于最小二乘法的自回归(AR)模型进行对比仿真验证,仿真结果表明,NKN-GPR模型在运动预测精度、平滑性、预测时长等方面具有显著优势,证明了所提算法的有效性,可为舰载机自动安全着舰提供理论支撑。