Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

An improved four-dimensional variation source term inversion model with observation error regularization

Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.

Simulation of Silty Clay Compressibility Parameters Based on Improved BP Neural Network Using Bayesian Regularization

Soil compressibility parameters are important indicators in the geotechnical field and are affected by various factors such as natural conditions and human interference.When the sample size is too large,conventional methods require massive human and financial resources.In order to reasonably simulate the compressibility parameters of the sample,this paper firstly adopts the correlation analysis to select seven influencing factors.Each of the factors has a high correlation with compressibility parameters.Meanwhile,the proportion of the weights of the seven factors in the Bayesian neural network is analyzed based on Garson theory.Secondly,an output model of the compressibility parameters of BR-BP silty clay is established based on Bayesian regularized BP neural network.Finally,the model is used to simulate the measured compressibility parameters.The output results are compared with the measured values and the output results of the traditional LM-BP neural network.The results show that the model is more stable and has stronger nonlinear fitting ability.The output of the model is basically consistent with the actual value.Compared with the traditional LMBP neural network model,its data sensitivity is enhanced,and the accuracy of the output result is significantly improved,the average value of the relative error of the compression coefficient is reduced from 15.54%to 6.15%,and the average value of the relative error of the compression modulus is reduced from 6.07%to 4.62%.The results provide a new technical method for obtaining the compressibility parameters of silty clay in this area,showing good theoretical significance and practical value.

L1/2 Regularization Based on Bayesian Empirical Likelihood

Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L1/2 regularization based on Bayesian empirical likelihood. The L1/2 penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.

Application of Bayesian regularized BP neural network model for analysis of aquatic ecological data—A case study of chlorophyll-a prediction in Nanzui water area of Dongting Lake

Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS i1.0 software, the BRBPNN model was established between chlorophyll-α and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.000？8426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll- α declined in the order of alga amount 〉 secchi disc depth（SD） 〉 electrical conductivity （EC）. Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-α concentration, total phosphorus（TP） and total nitrogen（TN） were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data（chlorophyll-α prediction） and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.

Bayesian Regularized Quantile Regression Analysis Based on Asymmetric Laplace Distribution

In recent years, variable selection based on penalty likelihood methods has aroused great concern. Based on the Gibbs sampling algorithm of asymmetric Laplace distribution, this paper considers the quantile regression with adaptive Lasso and Lasso penalty from a Bayesian point of view. Under the non-Bayesian and Bayesian framework, several regularization quantile regression methods are systematically compared for error terms with different distributions and heteroscedasticity. Under the error term of asymmetric Laplace distribution, statistical simulation results show that the Bayesian regularized quantile regression is superior to other distributions in all quantiles. And based on the asymmetric Laplace distribution, the Bayesian regularized quantile regression approach performs better than the non-Bayesian approach in parameter estimation and prediction. Through real data analyses, we also confirm the above conclusions.

The Smoothness of Weak Solutions to the System of Second Order Differential Equations with Non-negative Characteristics

In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.

Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization

Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.

Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.

基于Bayesian正则化BP神经网络的GPS高程转换

针对标准BP神经网络算法泛化能力弱、易过度训练等问题,应用Bayesian正则化算法改进BP神经网络的泛化能力。通过对某矿区GPS联测水准点拟合计算,并与L-M算法、多项式曲面拟合等方法比较,Bayesian正则化的BP神经网络拟合精度更高、更稳定、泛化能力更强。

Bayesian正规化BP神经网络及其在医学预测中的应用

目的提高BP神经网络的推广能力。方法采用正规化方法,利用MATLAB软件编程。结果实例分析表明Bayesian正规化BP神经网络模型不仅能准确地拟合训练值,而且能更合理地进行预测未知样本,具有较好的泛化能力。结论Bayesian正规化方法建立的BP神经网络可以提高其泛化能力,在小样本情况下更具应用价值。

常规公交风险的SEM与Bayesian Network组合评估方法研究

常规公交系统具有载客量大、班次多、线路固定等特点,存在多种安全风险隐患。为综合评估常规公交风险,对国内外554条事故数据分析整理,构建了常规公交风险指标体系。建立了常规公交风险评估的结构方程模型,得到常规公交风险因素对事故的单向拓扑结构。在结构学习的基础上,利用信息熵理论研究风险因素对预测结果可信度的影响权重,从而进行变量筛选。以失火事故为例利用贝叶斯网络模型进行了城市常规公交风险评估参数学习。研究结果表明,失火事故的主要风险因素为油气泄漏、车内外温度均较高等。在风险因素组合作用下失火事故发生概率范围为0.002 1至0.842 9。所建模型预测精度高,验证了方法的科学性和准确性,可用于进行定量化的常规公交风险评估。

基于Markov随机场和Bayesian理论的脑内磁源重建

1引言 基于脑磁图MEG的脑磁源成像,又可称电流密度重建或磁源分布图像重建,是一种新的检测神经电流活动特性的图像重构技术.它不是一个普通问题,而是跟诸如计算机视觉、地球物理等这些问题一样,是不定的或至少是病态的,从而推翻了当年Hadamard等人的认为不存在实际不定问题的论断.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

Conventional artificial neural networks used to solve electrical resistivity imaging （ERI） inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network （PBNN） nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter αk, which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

基于Bayesian正则化算法的非线性函数拟合

为克服常规BP算法在解决非线性函数拟合时泛化能力不强的问题,本文研究了用贝叶斯正则化算法来提高网络泛化能力的问题,结果表明在相同网络规模或误差条件下,Bayesian正则化算法泛化能力明显优于基本BP算法及其它改进的BP算法,且收敛速度较快,拟合效果好。

滚动轴承转速-振动深度学习模型的算法对比研究

轴承健康状况直接影响着机械设备的稳定性和安全性,对轴承的运行状态进行故障诊断尤为重要。基于此,在健康、内圈故障和外圈故障3种不同状况下,选择莱文贝格-马夸特(Levenberg-Marquardt,LM)算法、贝叶斯正则化(Bayesian Regularization,BR)算法和量化共轭梯度(Quantum Conjugate Gradient,QCG)算法,对在随时间变化的加速条件下滚动轴承振动数据进行训练和测试。在MATLAB R2023b软件中构建不同类型的深度学习模型,对比分析深度学习模型的均方误差值、回归R值、训练时长和训练轮数等多种指标。经过分析得出,在追求精度和准确性、内存资源和时间充足的情况下,应选用贝叶斯正则化法算法来训练深度学习网络模型。

Precipitation Retrieval from Himawari-8 Satellite Infrared Data Based on Dictionary Learning Method and Regular Term Constraint

In this paper,the application of an algorithm for precipitation retrieval based on Himawari-8 (H8) satellite infrared data is studied.Based on GPM precipitation data and H8 Infrared spectrum channel brightness temperature data,corresponding "precipitation field dictionary" and "channel brightness temperature dictionary" are formed.The retrieval of precipitation field based on brightness temperature data is studied through the classification rule of k-nearest neighbor domain (KNN) and regularization constraint.Firstly,the corresponding "dictionary" is constructed according to the training sample database of the matched GPM precipitation data and H8 brightness temperature data.Secondly,according to the fact that precipitation characteristics in small organizations in different storm environments are often repeated,KNN is used to identify the spectral brightness temperature signal of "precipitation" and "non-precipitation" based on "the dictionary".Finally,the precipitation field retrieval is carried out in the precipitation signal "subspace" based on the regular term constraint method.In the process of retrieval,the contribution rate of brightness temperature retrieval of different channels was determined by Bayesian model averaging (BMA) model.The preliminary experimental results based on the "quantitative" evaluation indexes show that the precipitation of H8 retrieval has a good correlation with the GPM truth value,with a small error and similar structure.

用Bayesian正则化BP神经网络预测稀土永磁体性能

针对一般BP神经网络泛化能力差,在Bayesian正则化BP神经网络的基础上,运用加权检验、"表决网"等方法的思路训练网络,并通过主成分分析方法对输入数据进行降维,建立了磁粉制备工艺(淬速度和晶化退火温度)、合金成分与磁性能之间的BPNN(back propagation network)预测模型。结果表明:该模型泛化能力较高,预测的Br相对误差在2%左右、Hcj和(BH)max都在5%以内,且每次预测的相对误差平均值波动不超过1%。

BAYESIAN METHOD OF MACROECONOMICAL DECISION

A Bayesian decision method is considered,which is applied to analysingthe reform problem of economic system in our country.When the number of eco-nomic departments satisfies some certain cunditions,the optinial lengths and optimalallocations are found in this paper.

Improved Non-negative Matrix Factorization Algorithm for Sparse Graph Regularization

Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.